Graphs - College Algebra
Card 1 of 380
Give the 
-coordinate of the 
-intercept of the graph of the function
Give the
Tap to reveal answer
The 
-intercept of the graph of a function is the point at which it intersects the 
-axis. The 
-coordinate is 0, so the 
-coordinate can be found by evaluating 
.
The function is piecewise-defined, so it is necessary to use the definition applicable for 
. However, the first definition applies for values of 
less than 0, and the second, for values greater. 
is undefined, and the graph of 
has no 
-intercept.
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
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Give the 
-coordinate(s) of the 
-intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of 
equal to 0 and solving for 
. For the first definition:
for 
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
for 
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore, 
has no solution, and the graph of 
has no 
-intercepts.
The
This necessitates setting both definitions of
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore,
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Give the -coordinate of the -intercept of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating .
The function is piecewise-defined, so it is necessary to use the definition applicable for . However, the first definition applies for values of less than 0, and the second, for values greater. is undefined, and the graph of has no -intercept.
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
← Didn't Know|Knew It →
Give the -coordinate(s) of the -intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of equal to 0 and solving for . For the first definition:
for
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
for
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore, has no solution, and the graph of has no -intercepts.
The
This necessitates setting both definitions of
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore,
← Didn't Know|Knew It →
Give the 
-coordinate(s) of the 
-intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of 
equal to 0 and solving for 
. For the first definition:
for 
Add 16:
By the Square Root Property:
or 
Since this definition holds only for 
, we only select 
.
For the second definition:
for 
Add 25:
By the Square Root Property:
or 
Since this definition holds only for 
, we only select 
.
Therefore, the graph has two 
-intercepts, which are at 
and 
.
The
This necessitates setting both definitions of
Add 16:
By the Square Root Property:
Since this definition holds only for
For the second definition:
Add 25:
By the Square Root Property:
Since this definition holds only for
Therefore, the graph has two
← Didn't Know|Knew It →
Give the -coordinate(s) of the -intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of equal to 0 and solving for . For the first definition:
for
Add 16:
By the Square Root Property:
or
Since this definition holds only for , we only select .
For the second definition:
for
Add 25:
By the Square Root Property:
or
Since this definition holds only for , we only select .
Therefore, the graph has two -intercepts, which are at and .
The
This necessitates setting both definitions of
Add 16:
By the Square Root Property:
Since this definition holds only for
For the second definition:
Add 25:
By the Square Root Property:
Since this definition holds only for
Therefore, the graph has two
← Didn't Know|Knew It →
Give the -coordinate(s) of the -intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of equal to 0 and solving for . For the first definition:
for
Add 16:
By the Square Root Property:
or
Since this definition holds only for , we only select .
For the second definition:
for
Add 25:
By the Square Root Property:
or
Since this definition holds only for , we only select .
Therefore, the graph has two -intercepts, which are at and .
The
This necessitates setting both definitions of
Add 16:
By the Square Root Property:
Since this definition holds only for
For the second definition:
Add 25:
By the Square Root Property:
Since this definition holds only for
Therefore, the graph has two
← Didn't Know|Knew It →
Give the 
-coordinate of the 
-intercept of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating 
.
The function is piecewise-defined, so it is necessary to use the definition applicable for 
. Since 
, and 
for 
. this is the definition to use.
The -intercept of the graph is the point 
.
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
The
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The above table refers to a function 
with domain 
.
Is this function even, odd, or neither?
The above table refers to a function
Is this function even, odd, or neither?
Tap to reveal answer
A function 
is odd if and only if, for every 
in its domain, 
; it is even if and only if, for every 
in its domain, 
.
We see that 
and 
. Therefore, 
, so is false for at least one 
. cannot be even.
For a function to be odd, since 
, it follows that 
; since 
is its own opposite, 
must be 0. However, 
; cannot be odd.
The correct choice is neither.
A function
We see that
For a function to be odd, since
The correct choice is neither.
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is a piecewise-defined function. Its definition is partially given below:
How can 
be defined for negative values of 
so that 
is an odd function?
How can
Tap to reveal answer
, by definition, is an odd function if, for all 
in its domain,
, or, equivalently 
One implication of this is that for 
to be odd, it must hold that 
. Since 
is explicitly defined to be equal to 0 here, this condition is satisfied.
Now, if 
is negative, 
is positive. it must hold that
,
so for all 
This is the correct choice.
One implication of this is that for
Now, if
so for all
This is the correct choice.
← Didn't Know|Knew It →
is a piecewise-defined function. Its definition is partially given below:
How can be defined for negative values of so that is an odd function?
How can
Tap to reveal answer
, by definition, is an odd function if, for all in its domain,
, or, equivalently
One implication of this is that for to be odd, it must hold that . If 
, then, since
for nonnegative values, then, by substitution,
This condition is satisfied.
Now, if is negative, is positive. it must hold that
,
so for all
,
the correct response.
One implication of this is that for
for nonnegative values, then, by substitution,
This condition is satisfied.
Now, if
so for all
the correct response.
← Didn't Know|Knew It →
Give the -coordinate(s) of the -intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of equal to 0 and solving for . For the first definition:
for
Add 16:
By the Square Root Property:
or
Since this definition holds only for , we only select .
For the second definition:
for
Add 25:
By the Square Root Property:
or
Since this definition holds only for , we only select .
Therefore, the graph has two -intercepts, which are at and .
The
This necessitates setting both definitions of
Add 16:
By the Square Root Property:
Since this definition holds only for
For the second definition:
Add 25:
By the Square Root Property:
Since this definition holds only for
Therefore, the graph has two
← Didn't Know|Knew It →
Give the -coordinate of the -intercept of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating .
The function is piecewise-defined, so it is necessary to use the definition applicable for . Since , and for . this is the definition to use.
The -intercept of the graph is the point .
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
The
← Didn't Know|Knew It →
The above table refers to a function with domain .
Is this function even, odd, or neither?
The above table refers to a function
Is this function even, odd, or neither?
Tap to reveal answer
A function is odd if and only if, for every in its domain, ; it is even if and only if, for every in its domain, .
We see that and . Therefore, , so is false for at least one . cannot be even.
For a function to be odd, since , it follows that ; since is its own opposite, must be 0. However, ; cannot be odd.
The correct choice is neither.
A function
We see that
For a function to be odd, since
The correct choice is neither.
← Didn't Know|Knew It →
is a piecewise-defined function. Its definition is partially given below:
How can be defined for negative values of so that is an odd function?
How can
Tap to reveal answer
, by definition, is an odd function if, for all in its domain,
, or, equivalently
One implication of this is that for to be odd, it must hold that . Since is explicitly defined to be equal to 0 here, this condition is satisfied.
Now, if is negative, is positive. it must hold that
,
so for all
This is the correct choice.
One implication of this is that for
Now, if
so for all
This is the correct choice.
← Didn't Know|Knew It →
is a piecewise-defined function. Its definition is partially given below:
How can be defined for negative values of so that is an odd function?
How can
Tap to reveal answer
, by definition, is an odd function if, for all in its domain,
, or, equivalently
One implication of this is that for to be odd, it must hold that . If , then, since
for nonnegative values, then, by substitution,
This condition is satisfied.
Now, if is negative, is positive. it must hold that
,
so for all
,
the correct response.
One implication of this is that for
for nonnegative values, then, by substitution,
This condition is satisfied.
Now, if
so for all
the correct response.
← Didn't Know|Knew It →
Give the -coordinate of the -intercept of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating .
The function is piecewise-defined, so it is necessary to use the definition applicable for . However, the first definition applies for values of less than 0, and the second, for values greater. is undefined, and the graph of has no -intercept.
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
← Didn't Know|Knew It →
Give the -coordinate(s) of the -intercept(s) of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by solving the equation
This necessitates setting both definitions of equal to 0 and solving for . For the first definition:
for
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
for
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore, has no solution, and the graph of has no -intercepts.
The
This necessitates setting both definitions of
However, this definition only holds for values less than 0. No solution is yielded.
For the second definition:
However, this definition only holds for values greater than or equal to 0. No solution is yielded.
Therefore,
← Didn't Know|Knew It →
Give the -coordinate of the -intercept of the graph of the function
Give the
Tap to reveal answer
The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating .
The function is piecewise-defined, so it is necessary to use the definition applicable for . Since , and for . this is the definition to use.
The -intercept of the graph is the point .
The
The function is piecewise-defined, so it is necessary to use the definition applicable for
The
← Didn't Know|Knew It →
is a piecewise-defined function. Its definition is partially given below:
How can be defined for negative values of so that is an odd function?
How can
Tap to reveal answer
, by definition, is an odd function if, for all in its domain,
, or, equivalently
One implication of this is that for to be odd, it must hold that . Since is explicitly defined to be equal to 0 here, this condition is satisfied.
Now, if is negative, is positive. it must hold that
,
so for all
This is the correct choice.
One implication of this is that for
Now, if
so for all
This is the correct choice.
← Didn't Know|Knew It →