Algebra - PSAT Math
Card 1 of 5075
Let f(x) be defined as follows:
What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as 
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = 
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, 
, is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to 
and multiply to 
.
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that 
.
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:
What is the value of
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Find all real solutions to the equation.
Find all real solutions to the equation.
Tap to reveal answer
To solve by factoring, we need two numbers that add to and multiply to .
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that .
To solve by factoring, we need two numbers that add to
In order for the equation to equal zero, one of the terms must be equal to zero.
OR
Our final answer is that
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: 
.
Thus, the domain for the inverse relation will also be 
.
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: .
Thus, the domain for the inverse relation will also be .
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: .
Thus, the domain for the inverse relation will also be .
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: .
Thus, the domain for the inverse relation will also be .
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: .
Thus, the domain for the inverse relation will also be .
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →
Given the relation below, identify the domain of the inverse of the relation.
Given the relation below, identify the domain of the inverse of the relation.
Tap to reveal answer
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: .
Thus, the domain for the inverse relation will also be .
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is:
Thus, the domain for the inverse relation will also be
← Didn't Know|Knew It →