Determine the Symmetry of an Equation - Pre-Calculus
Card 1 of 36
Is the following function symmetric across the y-axis? (Is it an even function?)
Is the following function symmetric across the y-axis? (Is it an even function?)
Tap to reveal answer
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute 
in for 
. When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.
For our function:
Thus the function is not symmetric about the y-axis.
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute
For our function:
Thus the function is not symmetric about the y-axis.
← Didn't Know|Knew It →
Is the following function symmetric across the y-axis? (Is it an even function?)
Is the following function symmetric across the y-axis? (Is it an even function?)
Tap to reveal answer
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute 
in for 
. When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.
For our function:
Since this matches the original, our function is symmetric across the y-axis.
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute
For our function:
Since this matches the original, our function is symmetric across the y-axis.
← Didn't Know|Knew It →
Determine if there is symmetry with the equation 
to the 
-axis and the method used to determine the answer.
Determine if there is symmetry with the equation
Tap to reveal answer
In order to determine if there is symmetry about the x-axis, replace all 
variables with 
. Solving for 
, if the new equation is the same as the original equation, then there is symmetry with the x-axis.
Since the original and new equations are not equivalent, there is no symmetry with the x-axis.
The correct answer is:
In order to determine if there is symmetry about the x-axis, replace all
Since the original and new equations are not equivalent, there is no symmetry with the x-axis.
The correct answer is:
← Didn't Know|Knew It →
Is the following function symmetrical about the y axis (is it an even function)?
Is the following function symmetrical about the y axis (is it an even function)?
Tap to reveal answer
For a function to be even, it must satisfy the equality 
Likewise if a function is even, it is symmetrical about the y-axis 
Therefore, the function is not even, and so the answer is No
For a function to be even, it must satisfy the equality
Likewise if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy 
so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy 
so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis
For a function to be symmetrical about the y-axis, it must satisfy 
For a function to be symmetrical about the x-axis, it must satisfy 
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy 
so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy 
so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin.
For a function to be symmetrical about the y-axis, it must satisfy 
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin.
← Didn't Know|Knew It →
Is the following function symmetrical about the y-axis (is it an even function)?
Is the following function symmetrical about the y-axis (is it an even function)?
Tap to reveal answer
For a function to be even, it must satisfy the equality 
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
For a function to be even, it must satisfy the equality
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
← Didn't Know|Knew It →
Which of the following best describes the symmetry of 
with respect to the x-axis, y-axis, and the origin.
Which of the following best describes the symmetry of 
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy 
so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy 
so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y-axis, and the origin. 
Algebraically check for symmetry with respect to the x-axis, y-axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy 
so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy 
so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".
← Didn't Know|Knew It →
Is the following function symmetrical about the y-axis (is it an even function)?
Is the following function symmetrical about the y-axis (is it an even function)?
Tap to reveal answer
For a function to be even, it must satisfy the equality
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
For a function to be even, it must satisfy the equality
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
← Didn't Know|Knew It →
Is the following function symmetric across the y-axis? (Is it an even function?)
Is the following function symmetric across the y-axis? (Is it an even function?)
Tap to reveal answer
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute in for . When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.
For our function:
Thus the function is not symmetric about the y-axis.
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute
For our function:
Thus the function is not symmetric about the y-axis.
← Didn't Know|Knew It →
Is the following function symmetric across the y-axis? (Is it an even function?)
Is the following function symmetric across the y-axis? (Is it an even function?)
Tap to reveal answer
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute in for . When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.
For our function:
Since this matches the original, our function is symmetric across the y-axis.
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute
For our function:
Since this matches the original, our function is symmetric across the y-axis.
← Didn't Know|Knew It →
Determine if there is symmetry with the equation to the -axis and the method used to determine the answer.
Determine if there is symmetry with the equation
Tap to reveal answer
In order to determine if there is symmetry about the x-axis, replace all variables with . Solving for , if the new equation is the same as the original equation, then there is symmetry with the x-axis.
Since the original and new equations are not equivalent, there is no symmetry with the x-axis.
The correct answer is:
In order to determine if there is symmetry about the x-axis, replace all
Since the original and new equations are not equivalent, there is no symmetry with the x-axis.
The correct answer is:
← Didn't Know|Knew It →
Is the following function symmetrical about the y axis (is it an even function)?
Is the following function symmetrical about the y axis (is it an even function)?
Tap to reveal answer
For a function to be even, it must satisfy the equality
Likewise if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No
For a function to be even, it must satisfy the equality
Likewise if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin.
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin.
← Didn't Know|Knew It →
Which of the following best describes the symmetry of with respect to the x-axis, y-axis, and the origin.
Which of the following best describes the symmetry of
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy
so there is not symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
so there is symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.
← Didn't Know|Knew It →
Algebraically check for symmetry with respect to the x-axis, y-axis, and the origin.
Algebraically check for symmetry with respect to the x-axis, y-axis, and the origin.
Tap to reveal answer
For a function to be symmetrical about the y-axis, it must satisfy
so there is symmetry about the y-axis
For a function to be symmetrical about the x-axis, it must satisfy
so there is not symmetry about the x-axis
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".
For a function to be symmetrical about the y-axis, it must satisfy
For a function to be symmetrical about the x-axis, it must satisfy
For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.
So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".
← Didn't Know|Knew It →
Is the following function symmetrical about the y-axis (is it an even function)?
Is the following function symmetrical about the y-axis (is it an even function)?
Tap to reveal answer
For a function to be even, it must satisfy the equality
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
For a function to be even, it must satisfy the equality
Likewise, if a function is even, it is symmetrical about the y-axis
Therefore, the function is not even, and so the answer is No.
← Didn't Know|Knew It →
Is the following function symmetric across the y-axis? (Is it an even function?)
Is the following function symmetric across the y-axis? (Is it an even function?)
Tap to reveal answer
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute in for . When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.
For our function:
Thus the function is not symmetric about the y-axis.
One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute
For our function:
Thus the function is not symmetric about the y-axis.
← Didn't Know|Knew It →