Question

use the drawing tool(s) to form the correct answer on the provided graph.
graph the composite function g(f(x)).
$f(x) = -2x$
$g(x) = \frac{1}{2}x + 3$

Explanation:

Step1: Substitute $f(x)$ into $g(x)$

$g(f(x)) = g(-2x)$

Step2: Compute the composite function

$g(f(x)) = \frac{1}{2}(-2x) + 3 = -x + 3$

Step3: Identify key points for graphing

When $x=0$, $g(f(0)) = 3$; when $g(f(x))=0$, $x=3$. So we have points $(0, 3)$ and $(3, 0)$.

Answer:

The composite function is $g(f(x)) = -x + 3$. To graph it:

1. Plot the y-intercept point $(0, 3)$
2. Plot the x-intercept point $(3, 0)$
3. Draw a straight line connecting these two points, extending it across the grid.