Graphing - Geometry
Card 1 of 832
Give the range of the function
.
Give the range of the function
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Let 
A logarithm can take any real value. Therefore, the range of 
is the set of real numbers, as is any linear transformation of 
.
In terms of 
,
making 
such a transformation. This makes the range of 
the set of all real numbers.
Let
A logarithm can take any real value. Therefore, the range of
In terms of
making
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Give the domain of the function 
.
Give the domain of the function
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Let 
. This function is defined for any real number 
, so the domain of 
is the set of all real numbers. In terms of 
,
Since 
is defined for all real 
, so is 
; it follows that 
is as well. The correct domain is the set of all real numbers.
Let
Since
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A triangle is made up of the following points:
What are the points of the inverse triangle?
A triangle is made up of the following points:
What are the points of the inverse triangle?
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The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, 
has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation
However, there is no real number 
for which this equation holds, as the square of any such number must be positive. Therefore, the domain of 
does not exclude any real values, and the domain is the set of all real numbers.
As a rational function,
However, there is no real number
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Give the range of the function
.
Give the range of the function
Tap to reveal answer
Let
A logarithm can take any real value. Therefore, the range of is the set of real numbers, as is any linear transformation of .
In terms of ,
making such a transformation. This makes the range of the set of all real numbers.
Let
A logarithm can take any real value. Therefore, the range of
In terms of
making
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Give the domain of the function 
.
Give the domain of the function
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is a polynomial function, and as such has the set of all real numbers as its domain.
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Give the domain of the function
Give the domain of the function
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The domain of any polynomial function, such as 
, is the set of real numbers, as a polynomial can be evaluated for any real value of 
.
The domain of any polynomial function, such as
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, 
has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation:
The domain excludes only the value 
- that is, the domain is 
.
As a rational function,
The domain excludes only the value
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation
However, there is no real number for which this equation holds, as the square of any such number must be positive. Therefore, the domain of does not exclude any real values, and the domain is the set of all real numbers.
As a rational function,
However, there is no real number
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Give the domain of the function .
Give the domain of the function
Tap to reveal answer
is a polynomial function, and as such has the set of all real numbers as its domain.
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation:
The domain excludes only the value - that is, the domain is .
As a rational function,
The domain excludes only the value
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation
However, there is no real number for which this equation holds, as the square of any such number must be positive. Therefore, the domain of does not exclude any real values, and the domain is the set of all real numbers.
As a rational function,
However, there is no real number
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Give the domain of the function .
Give the domain of the function
Tap to reveal answer
is a polynomial function, and as such has the set of all real numbers as its domain.
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A triangle is made up of the following points:
What are the points of the inverse triangle?
A triangle is made up of the following points:
What are the points of the inverse triangle?
Tap to reveal answer
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
← Didn't Know|Knew It →
A triangle is made up of the following points:
What are the points of the inverse triangle?
A triangle is made up of the following points:
What are the points of the inverse triangle?
Tap to reveal answer
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
The inverse of a function has all the same points as the original function, except the x values and y values are reversed. The same rule applies to polygons such as triangles.
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Give the domain of the function
Give the domain of the function
Tap to reveal answer
The domain of any polynomial function, such as , is the set of real numbers, as a polynomial can be evaluated for any real value of .
The domain of any polynomial function, such as
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Give the domain of the function
Give the domain of the function
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There is no restriction on the value of 
, as a cube root can be taken of any real number, regardless of sign. Since 
is not restricted in value, neither is 
, and the domain of 
is the set of real numbers.
There is no restriction on the value of
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Give the domain of the function
.
Give the domain of the function
Tap to reveal answer
As a rational function, has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation
However, there is no real number for which this equation holds, as the square of any such number must be positive. Therefore, the domain of does not exclude any real values, and the domain is the set of all real numbers.
As a rational function,
However, there is no real number
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Give the domain of the function
Give the domain of the function
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The function 
is defined for those values of 
for which the radicand is nonnegative - that is, for which
Subtract 25 from both sides:
Since the square root of a real number is always nonnegative,
for all real numbers 
. Since the radicand is always positive, this makes the domain of 
the set of all real numbers.
The function
Subtract 25 from both sides:
Since the square root of a real number is always nonnegative,
for all real numbers
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Give the domain of the function .
Give the domain of the function
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is a polynomial function, and as such has the set of all real numbers as its domain.
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