Question

graph for the following linear function. f(x) = -3(2 - x)

Explanation:

Step1: Simplify the function

$f(x) = -3(2 - x) = -6 + 3x = 3x - 6$

Step2: Find y-intercept (x=0)

$f(0) = 3(0) - 6 = -6$

Step3: Find x-intercept (f(x)=0)

$0 = 3x - 6 \implies 3x = 6 \implies x = 2$

Step4: Identify slope

The function is in $y=mx+b$ form, so slope $m=3$

Answer:

This linear function simplifies to $f(x)=3x-6$. It has a y-intercept at $(0, -6)$, an x-intercept at $(2, 0)$, and a positive slope of 3 (the line rises 3 units for every 1 unit it moves right). To graph it, plot the two intercept points and draw a straight line through them.