Question

Which of the following correctly describes the symmetry of the cubic parent
function?
^
A. It is symmetric about the x-axis.
B. It is symmetric about the y-axis.
C. It is symmetric about the origin.
D. It is not symmetric about any point or line.

Answer 1

Answer:

Note: By definition, no function can be symmetric about the x-axis (or any ... B: the graph of an hyperbola ... C: the graph of a cubic ... Graph D: This cubic is centered at the point (0, –3).

Answer 2

The statement that correctly describes  the symmetry of the cubic parent function is 'It is symmetric about the origin.'

The correct answer is option (c)

What is the symmetry of the function about the X-axis?

"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (a, -b) "

What is the symmetry of the function about the Y-axis?

"The graph of the function is said to be symmetric about Y-axis if whenever (a, b) is on the graph then so is (-a, b) "

What is the symmetry of the function about the origin?

"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (-a, -b) "

For given question,

The parent cubic function is $f(x)=x^3$

The graph of the function  $f(x)=x^3$ is as shown below.

From graph we can observe that, point (x, y) as well as (-x, -y) is on the graph.

This means, the graph of  the function  $f(x)=x^3$ is symmetric about the origin.

Therefore, the statement that correctly describes  the symmetry of the cubic parent function is 'It is symmetric about the origin.'

The correct answer is option (c)

Learn more about the symmetry of the function here:

https://brainly.com/question/11957987

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