Question

The graph of F(x) shown below resembles the graph of G(x)=x^4 , but is has been flipped over the x-axis. Which of the following is the equation of F(x)?

Answer 1

Answer: $F(x)\text{ = -x}^4\text{ \lparen option D\rparen}$

Explanation:

Given:

The function of f(x) resembles the function G(x) with a reflection over the x-axis

$G(x)\text{ = x}^4$

To find:

the function of f(x)

A reflection over the x-axis is given as:

$\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen x, -y\rparen} \\ This\text{ means we will negate the y coordinate while keeping the x coodinate constant} \\ \\ It\text{ is also written as -f\lparen x\rparen} \\ In\text{ this case, it will be -G\lparen x\rparen} \end{gathered}$$F(x)\text{ = -x}^4\text{ \lparen option D\rparen}$