Question

which graph represents the situation $h(x) = f(x) - g(x)$?

Explanation:

Step1: Define linear functions

First, identify equations for $f(x)$ and $g(x)$ from their graphs.

• $f(x)$ is a horizontal line: $f(x) = 1$
• $g(x)$ has slope $1$, y-intercept $0$: $g(x) = x$

Step2: Calculate $h(x)=f(x)-g(x)$

Substitute the functions into the formula.
$h(x) = 1 - x$

Step3: Analyze $h(x)$ properties

$h(x)=-x+1$ has:

• Slope $-1$ (decreasing line)
• Y-intercept $(0,1)$
• X-intercept $(1,0)$

Answer:

The third graph (with the downward-sloping $h(x)$ line passing through $(0,1)$ and $(1,0)$)