Question

consider the function shown to the left.
$g(x) = -\frac{1}{2}x + 5$
evaluate $g(6) = $
evaluate $g(-14) = $
find the value of $x$ that makes $g(x) = 7$.
$x = $

Explanation:

Part 1: Evaluate \( g(6) \)

Step 1: Substitute \( x = 6 \) into \( g(x) \)

We have the function \( g(x)=-\frac{1}{2}x + 5 \). Substitute \( x = 6 \) into the function:
\( g(6)=-\frac{1}{2}(6)+5 \)

Step 2: Simplify the expression

First, calculate \( -\frac{1}{2}(6)=-3 \). Then add 5:
\( g(6)=-3 + 5=2 \)

Part 2: Evaluate \( g(-14) \)

Step 1: Substitute \( x=-14 \) into \( g(x) \)

Substitute \( x = - 14 \) into \( g(x)=-\frac{1}{2}x + 5 \):
\( g(-14)=-\frac{1}{2}(-14)+5 \)

Step 2: Simplify the expression

First, calculate \( -\frac{1}{2}(-14) = 7 \). Then add 5:
\( g(-14)=7 + 5=12 \)

Part 3: Find \( x \) when \( g(x) = 7 \)

Step 1: Set up the equation

We know that \( g(x)=-\frac{1}{2}x + 5 \) and \( g(x) = 7 \). So we set up the equation:
\( -\frac{1}{2}x+5 = 7 \)

Step 2: Solve for \( x \)

Subtract 5 from both sides:
\( -\frac{1}{2}x=7 - 5=2 \)
Multiply both sides by - 2:
\( x=2\times(-2)=-4 \)

Answer:

s:

• \( g(6)=\boldsymbol{2} \)
• \( g(-14)=\boldsymbol{12} \)
• The value of \( x \) when \( g(x) = 7 \) is \( \boldsymbol{-4} \)