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We are given two functions:

\[
p(x) = -4x - 4
\]
\[
q(x) = 2x + 5
\]

We are asked to evaluate the following composite functions:

1. \((q \circ p)(2)\), which means \(q(p(2))\)
2. \((p \circ q)(2)\), which means \(p(q(2))\)

### Step 1: Calculate \(p(2)\)

\[
p(2) = -4(2) - 4 = -8 - 4 = -12
\]

### Step 2: Calculate \(q(p(2)) = q(-12)\)

\[
q(-12) = 2(-12) + 5 = -24 + 5 = -19
\]

Thus, \((q \circ p)(2) = -19\).

### Step 3: Calculate \(q(2)\)

\[
q(2) = 2(2) + 5 = 4 + 5 = 9
\]

### Step 4: Calculate \(p(q(2)) = p(9)\)

\[
p(9) = -4(9) - 4 = -36 - 4 = -40
\]

Thus, \((p \circ q)(2) = -40\).

### Final Answers:
- \((q \circ p)(2) = -19\)
- \((p \circ q)(2) = -40\)

Would you like more details or have any questions?

Here are five related questions you can explore:
1. How would you calculate \((p \circ p)(2)\)?
2. Can you compute \((q \circ q)(2)\)?
3. What are the steps to find \((p \circ q)(x)\) in general form?
4. How does the order of composition affect the result (e.g., why \((p \circ q)(2) \neq (q \circ p)(2)\))?
5. What is the domain of \(p(x)\) and \(q(x)\) for compositions?

**Tip:** When performing function compositions, always evaluate the inside function first and then substitute that result into the outer function.

Find the values of (q ∘ p)(2) and (p ∘ q)(2) given p(x) = -4x - 4 and q(x) = 2x + 5.

Learn how to compute function compositions with linear functions. Given p(x) = -4x - 4 and q(x) = 2x + 5, find (q ∘ p)(2) and (p ∘ q)(2) using step-by-step calculations. Suitable for students in Grades 9-11.

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