Question

1. russell is looking at two functions. the first function is represented by the equation: ( f(x) = -\frac{1}{2}x + 2 ). the second function is represented by the graph. which function has the largest ( y )-value when ( x = -4 )?

( \bigcirc ) ( g(x) )
( \bigcirc ) ( f(x) )

Explanation:

Step1: Find \( f(-4) \)

Given \( f(x)=-\frac{1}{2}x + 2 \), substitute \( x = -4 \):
\( f(-4)=-\frac{1}{2}(-4)+2 \)
\( = 2 + 2 = 4 \)

Step2: Find \( g(-4) \)

From the graph of \( g(x) \), it's a line. Let's find its equation. The line passes through \( (0, 6) \) and \( (6, 0) \). Slope \( m=\frac{0 - 6}{6 - 0}=-1 \). Equation: \( g(x)=-x + 6 \). Substitute \( x = -4 \):
\( g(-4)=-(-4)+6 = 4 + 6 = 10 \)

Step3: Compare \( f(-4) \) and \( g(-4) \)

\( f(-4)=4 \), \( g(-4)=10 \). Since \( 10>4 \), \( g(x) \) has a larger \( y \)-value at \( x = -4 \).

Answer:

\( g(x) \)