Chapter 2.2, Problem 48AYU

To determine

To find: A function whose graph is symmetric with respect to the x-axis.

Answer to Problem 48AYU

The function whose graph is symmetric with respect to the x-axis is $f\left(x\right)=-f\left(x\right)$ .

Explanation of Solution

Given information: Is there a function whose graph is symmetric with respect to the x-axis.

Calculation: If we replace y with −y and simplify the equation and if the resulting equation is equivalent to the original equation then the graph is symmetric about x-axis.

Since, The graph of the function is symmetric with respect to the x-axis.

Therefore, The function should be $f\left(x\right)=-f\left(x\right)$ .

Hence, The function whose graph is symmetric with respect to the x-axis is $f\left(x\right)=-f\left(x\right)$ .