Question

1. the parent linear function is $f(x)=x$

the transformation of the parent function is graphed as $g(x)$ shown below. which equation matches the transformation shown in
the graph?
a. $g(x)=3x$
b. $g(x)=\frac{3}{2}x$
c. $g(x)=\frac{2}{3}x$
d. $g(x)=2x$
e. $g(x)=-3x$

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line through points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). The parent function \( f(x)=x \) has a slope of 1. For \( g(x) \), we can pick two points. From the graph, let's use \((0,0)\) and \((3,2)\) (or other points, but these are clear).

Step2: Calculate slope of \( g(x) \)

Using \( (x_1,y_1)=(0,0) \) and \( (x_2,y_2)=(3,2) \), the slope \( m=\frac{2 - 0}{3 - 0}=\frac{2}{3} \). So the equation of \( g(x) \) is \( g(x)=\frac{2}{3}x \) since it passes through the origin (y - intercept is 0).

Answer:

C. \( g(x)=\frac{2}{3}x \)