Question

Help me solve this hw problem pls formula for getting g(x)

Answer 1

Step-by-step explanation:

Given:

A graph of f(x) in red and a graph of g(x) in blue

To find:

the formula for getting g(x)

First, we need to determine the function for f(x) from the graph

The roots of the function for f(x) are -4, 0, 4

The line crosses the x axis at x = -4, x = 0 and x = 4

x + 4 = 0, x - 0 = 0, x - 4 = 0

The factors: (x + 4)(x - 0)(x - 4)

`\begin{gathered} f(x)\text{ = \lparen x + 4\rparen\lparen x\rparen\lparen x - 4\rparen} \\ Expanding\text{ the function:} \\ f(x)\text{ = \lparen x}^2\text{ + 4x\rparen\lparen x - 4\rparen} \\ f(x)\text{ = x}^2(x\text{ - 4\rparen + 4x\lparen x - 4\rparen} \\ f(x)\text{ = x}^3\text{ - 4x}^2\text{ + 4x}^2\text{ - 16x} \\ f(x)\text{ = x}^3\text{ - 16x} \end{gathered}`

Comparing the coordinates of f(x) and g(x):

`\begin{gathered} From\text{ the graph of g\lparen x\rparen in blue} \\ when\text{ x = -4, y = 3, g\lparen x\rparen} \\ \text{ when x = 0, y = 0 f\lparen x\rparen} \\ \\ when\text{ x = 2, y = 2 g\lparen x\rparen} \\ when\text{ x = 2, y = -4 f\lparen x\rparen} \\ \\ when\text{ x = 4, y = 0 f\lparen x\rparen} \\ when\text{ x= 4, y = 3 g\lparen x\rparen} \end{gathered}`