To graph $h(x) = (f + g)(x)$, we need to add the corresponding values of the functions $f(x)$ and $g(x)$ at each $x$-coordinate and plot the resulting points. Let's analyze the graphs step-by-step.

Step 1: Identify key points for $f(x)$ and $g(x)$

For function $f(x)$ (top graph):

• $f(-3) = 0$
• $f(-2) = 2$
• $f(0) = 3$
• $f(2) = 2$
• $f(3) = 0$

For function $g(x)$ (bottom graph):

• $g(-3) = -3$
• $g(-2) = 0$
• $g(0) = -1$
• $g(2) = 1$
• $g(3) = 2$

Step 2: Compute $h(x) = f(x) + g(x)$ for each $x$-value

• $h(-3) = f(-3) + g(-3) = 0 + (-3) = -3$
• $h(-2) = f(-2) + g(-2) = 2 + 0 = 2$
• $h(0) = f(0) + g(0) = 3 + (-1) = 2$
• $h(2) = f(2) + g(2) = 2 + 1 = 3$
• $h(3) = f(3) + g(3) = 0 + 2 = 2$

Step 3: Plot the points for $h(x)$

You need to plot the points:

• $(-3, -3)$
• $(-2, 2)$
• $(0, 2)$
• $(2, 3)$
• $(3, 2)$

After plotting these points, connect them with line segments to complete the graph of $h(x)$.

Would you like further details on how to graph this, or help with any other part?

Here are 5 related questions to expand on this topic:

1. How do you determine the domain and range of $h(x)$?
2. What happens when you subtract two functions instead of adding them?
3. Can you interpret the meaning of the intersection points between $f(x)$ and $g(x)$?
4. What would the graph look like if $f(x)$ were multiplied by a scalar before adding to $g(x)$?
5. How do transformations (like shifting or stretching) affect the sum of two functions?

Tip: When graphing, it can help to use a table of values to ensure accuracy before drawing the segments.