Symmetry - College Algebra
Card 0 of 48
Which of the following is true of the relation graphed above?
Which of the following is true of the relation graphed above?
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it is seen to be symmetric about the origin. Consequently, for each 
in the domain, 
- the function is odd.
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it is seen to be symmetric about the origin. Consequently, for each
Compare your answer with the correct one above
Define 
.
Is this function even, odd, or neither?
Define
Is this function even, odd, or neither?
A function 
is odd if and only if, for all 
, 
; it is even if and only if, for all 
, 
. Therefore, to answer this question, determine 
by substituting 
for 
, and compare it to both 
and 
.
, so 
is not even.
, so 
is not odd.
A function
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is an even function; 
.
True or false: It follows that 
.
True or false: It follows that
A function is even if and only if, for all 
in its domain, 
. It follows that if 
, then
.
No restriction is placed on any other value as a result of this information, so the answer is false.
A function
No restriction is placed on any other value as a result of this information, so the answer is false.
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is an even function. Let 
.
Is 
an even function, an odd function, or neither?
Is
A function 
is even if, for each 
in its domain,
.
It is odd if, for each 
in its domain,
.
Substitute 
for 
in the definition of 
:
Since is even, 
, so
This makes 
an odd function.
A function
It is odd if, for each
Substitute
Since
This makes
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Determine the symmetry of the following equation.
Determine the symmetry of the following equation.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace 
.
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute 
.
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute 
, and 
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
Compare your answer with the correct one above
Which of the following is true of the relation graphed above?
Which of the following is true of the relation graphed above?
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each in the domain, 
- the function is odd.
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each
Compare your answer with the correct one above
Consider the relation graphed above. Which is true of this relation?
Consider the relation graphed above. Which is true of this relation?
The relation passes the Vertical Line test, as seen in the diagram below, in that no vertical line can be drawn that intersects the graph than once:
An function is odd if and only if its graph is symmetric about the origin, and even if and only if its graph is symmetric about the 
-axis. From the diagram, we see neither is the case.
The relation passes the Vertical Line test, as seen in the diagram below, in that no vertical line can be drawn that intersects the graph than once:
An function is odd if and only if its graph is symmetric about the origin, and even if and only if its graph is symmetric about the
Compare your answer with the correct one above
Which of the following is symmetrical to 
across the origin?
Which of the following is symmetrical to
Symmetry across the origin is symmetry across 
.
Determine the inverse of the function. Swap the x and y variables, and solve for y.
Subtract 3 on both sides.
Divide by negative two on both sides.
The answer is: 
Symmetry across the origin is symmetry across
Determine the inverse of the function. Swap the x and y variables, and solve for y.
Subtract 3 on both sides.
Divide by negative two on both sides.
The answer is:
Compare your answer with the correct one above
Consider the function 
.
Is 
an even function, an odd function, or neither?
Consider the function
Is
A function is even if, for each in its domain,
.
It is odd if, for each in its domain,
.
Substitute 
for 
in the definition:
Since 
, 
is an even function.
A function
It is odd if, for each
Substitute
Since
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Which of the following is true of the relation graphed above?
Which of the following is true of the relation graphed above?
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it is seen to be symmetric about the origin. Consequently, for each in the domain, - the function is odd.
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it is seen to be symmetric about the origin. Consequently, for each
Compare your answer with the correct one above
Define .
Is this function even, odd, or neither?
Define
Is this function even, odd, or neither?
A function is odd if and only if, for all , ; it is even if and only if, for all , . Therefore, to answer this question, determine by substituting for , and compare it to both and .
, so is not even.
, so is not odd.
A function
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is an even function; .
True or false: It follows that .
True or false: It follows that
A function is even if and only if, for all in its domain, . It follows that if , then
.
No restriction is placed on any other value as a result of this information, so the answer is false.
A function
No restriction is placed on any other value as a result of this information, so the answer is false.
Compare your answer with the correct one above
is an even function. Let .
Is an even function, an odd function, or neither?
Is
A function is even if, for each in its domain,
.
It is odd if, for each in its domain,
.
Substitute for in the definition of :
Since is even, , so
This makes an odd function.
A function
It is odd if, for each
Substitute
Since
This makes
Compare your answer with the correct one above
Determine the symmetry of the following equation.
Determine the symmetry of the following equation.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace .
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute .
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute , and
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
Compare your answer with the correct one above
Which of the following is true of the relation graphed above?
Which of the following is true of the relation graphed above?
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each in the domain, - the function is odd.
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each
Compare your answer with the correct one above
Consider the relation graphed above. Which is true of this relation?
Consider the relation graphed above. Which is true of this relation?
The relation passes the Vertical Line test, as seen in the diagram below, in that no vertical line can be drawn that intersects the graph than once:
An function is odd if and only if its graph is symmetric about the origin, and even if and only if its graph is symmetric about the -axis. From the diagram, we see neither is the case.
The relation passes the Vertical Line test, as seen in the diagram below, in that no vertical line can be drawn that intersects the graph than once:
An function is odd if and only if its graph is symmetric about the origin, and even if and only if its graph is symmetric about the
Compare your answer with the correct one above
Which of the following is symmetrical to across the origin?
Which of the following is symmetrical to
Symmetry across the origin is symmetry across .
Determine the inverse of the function. Swap the x and y variables, and solve for y.
Subtract 3 on both sides.
Divide by negative two on both sides.
The answer is:
Symmetry across the origin is symmetry across
Determine the inverse of the function. Swap the x and y variables, and solve for y.
Subtract 3 on both sides.
Divide by negative two on both sides.
The answer is:
Compare your answer with the correct one above
Consider the function .
Is an even function, an odd function, or neither?
Consider the function
Is
A function is even if, for each in its domain,
.
It is odd if, for each in its domain,
.
Substitute for in the definition:
Since , is an even function.
A function
It is odd if, for each
Substitute
Since
Compare your answer with the correct one above
Determine the symmetry of the following equation.
Determine the symmetry of the following equation.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace .
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute .
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute , and
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
To check for symmetry, we are going to do three tests, which involve substitution. First one will be to check symmetry along the x-axis, replace
This isn't equivilant to the first equation, so it's not symmetric along the x-axis.
Next is to substitute
This is not the same, so it is not symmetric along the y-axis.
For the last test we will substitute
This isn't the same as the orginal equation, so it is not symmetric along the origin.
The answer is it is not symmetric along any axis.
Compare your answer with the correct one above
Which of the following is true of the relation graphed above?
Which of the following is true of the relation graphed above?
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each in the domain, - the function is odd.
The relation graphed is a function, as it passes the vertical line test - no vertical line can pass through it more than once, as is demonstrated below:
Also, it can be seen to be symmetrical about the origin. Consequently, for each
Compare your answer with the correct one above