Chapter 3.1, Problem 18E

To determine

To find: whether graph of $f\left(x\right)$ is symmetric with respect to origin.

Answer to Problem 18E

Symmetric

Explanation of Solution

Given information:

  $f\left(x\right)=-7x^5+8$

Calculation:

Let’s check whether $f\left(-x\right)$ is equal to $-f\left(x\right)$ or not by substituting replacing x with $-x$ as shown below.

$f\left(x\right)=-7x^5+8$
Value of $x$	$f\left(x\right)$	$f\left(-x\right)$	$-f\left(x\right)$
$-x$	$7x^5+8$	$7x^5+8$	$7x^5+8$

Since, $f\left(-x\right)$ is equal to $-f\left(x\right)$ . Thus the graph is symmetric to the origin.