In Exercises 4 and 5 , use the graphs of $f$ and $h$ to describe the transformation from the graph of $f$ to the grap of $h$.
\[
f(x)=\frac{1}{3} x+1 ; h(x)=-f(x)
\]
Answer
\(\boxed{\text{The graph of } h(x) \text{ is the graph of } f(x) \text{ reflected in the x-axis}}\)
Step 1 ：Given the functions \(f(x)=\frac{1}{3} x+1\) and \(h(x)=-f(x)\)
Step 2 ：Substitute \(f(x)\) into \(h(x)\) to get \(h(x)=-\frac{1}{3} x-1\)
Step 3 ：The negative sign in front of the function \(f(x)\) in the definition of \(h(x)\) indicates a reflection in the x-axis
Step 4 ：This means that every point \((x, y)\) on the graph of \(f\) is transformed to the point \((x, -y)\) on the graph of \(h\)
Step 5 ：\(\boxed{\text{The graph of } h(x) \text{ is the graph of } f(x) \text{ reflected in the x-axis}}\)
