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Let's go through the problem step by step:

### Part (a): \((f + h)(0)\)

You need to find \((f + h)(0)\), which means adding the values of the functions \(f(x)\) and \(h(x)\) at \(x = 0\).

- From the graph of \(f(x)\), you can see that \(f(0)\) corresponds to the point on the graph where \(x = 0\). By looking at the graph, we can estimate that \(f(0) = -2\).
  
- From the table, \(h(0)\) is given directly as \(h(0) = 2\).

Now, calculate:
\[
(f + h)(0) = f(0) + h(0) = -2 + 2 = 0
\]

### Part (b): \(\left(\frac{h}{g}\right)(-1)\)

This expression requires you to divide \(h(-1)\) by \(g(-1)\).

- From the table, \(h(-1) = 0.5\).
- The function \(g(x) = 1 - x - x^2\) is provided. To find \(g(-1)\), substitute \(x = -1\) into \(g(x)\):
  \[
  g(-1) = 1 - (-1) - (-1)^2 = 1 + 1 - 1 = 1
  \]

Now, calculate:
\[
\left(\frac{h}{g}\right)(-1) = \frac{h(-1)}{g(-1)} = \frac{0.5}{1} = 0.5
\]

### Final answers:
(a) \((f + h)(0) = 0\)  
(b) \(\left(\frac{h}{g}\right)(-1) = 0.5\)

Would you like more details on any step?

Here are 5 questions to expand your understanding:
1. How would you evaluate \( (f - h)(0) \)?
2. What is \( g(0) \) and how does it affect other calculations?
3. How would you graph the function \( g(x) \)?
4. What is the domain and range of the function \( f(x) \) based on the graph?
5. How would the solution change if \( f(x) \) was modified slightly?

**Tip**: When combining functions, always check the values carefully from graphs, tables, or equations!

Consider the following problem with functions f(x), h(x), and g(x). Part (a) asks for the sum (f + h)(0), and Part (b) asks for the result of (h / g)(-1).

This page explores how to solve a two-part function operations problem involving the functions f(x), h(x), and g(x). Learn how to evaluate (f + h)(0) using graph interpretation and table lookup, as well as (h/g)(-1) through substitution into g(x). Suitable for students in Grades 9-12.

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