https://file.aiquickdraw.com/mathbot/file/1726502625668vzslfeyd.jpg

I can see the image you uploaded contains several functions that need to be evaluated. Let's break them down and solve each step by step.

### 1. **First Box:**
\[ f(y) = 3 - \sqrt{y}, \quad f(36) \]

We substitute \( y = 36 \):
\[
f(36) = 3 - \sqrt{36} = 3 - 6 = -3
\]

### 2. **Second Box:**
\[ f(x) = \frac{|3x|}{x}, \quad f(-6) \]

We substitute \( x = -6 \):
\[
f(-6) = \frac{|3(-6)|}{-6} = \frac{18}{-6} = -3
\]

### 3. **Third Box:**
\[ f(x) = 2x + 2, \quad f(-8) \]

Substituting \( x = -8 \):
\[
f(-8) = 2(-8) + 2 = -16 + 2 = -14
\]

### 4. **Fourth Box:**
\[ f(x) = -x^2 + 2, \quad f(-4) \]

Substituting \( x = -4 \):
\[
f(-4) = -(-4)^2 + 2 = -16 + 2 = -14
\]

### 5. **Fifth Box:**
\[ f(t) = \frac{2t^2 + 8}{t}, \quad f(4) \]

Substituting \( t = 4 \):
\[
f(4) = \frac{2(4)^2 + 8}{4} = \frac{2(16) + 8}{4} = \frac{32 + 8}{4} = \frac{40}{4} = 10
\]

### 6. **Sixth Box:**
\[ f(x) = \sqrt{x^2 - 17} + 2, \quad f(-9) \]

Substituting \( x = -9 \):
\[
f(-9) = \sqrt{(-9)^2 - 17} + 2 = \sqrt{81 - 17} + 2 = \sqrt{64} + 2 = 8 + 2 = 10
\]

### 7. **Seventh Box:**
\[ f(x) = -|x|^3 + 2, \quad f(-2) \]

Substituting \( x = -2 \):
\[
f(-2) = -|-2|^3 + 2 = -(2^3) + 2 = -(8) + 2 = -8 + 2 = -6
\]

### 8. **Eighth Box:**
\[ f(t) = -\sqrt{t^2 + 11}, \quad f(5) \]

Substituting \( t = 5 \):
\[
f(5) = -\sqrt{(5)^2 + 11} = -\sqrt{25 + 11} = -\sqrt{36} = -6
\]

---

### Summary of Results:
1. \( f(36) = -3 \)
2. \( f(-6) = -3 \)
3. \( f(-8) = -14 \)
4. \( f(-4) = -14 \)
5. \( f(4) = 10 \)
6. \( f(-9) = 10 \)
7. \( f(-2) = -6 \)
8. \( f(5) = -6 \)

Would you like a detailed explanation of any specific solution? Here are five related questions you could explore:

1. What are the properties of absolute value functions?
2. How do square root functions behave for positive and negative values?
3. What are the implications of squaring negative values in a function?
4. Can you explain how to simplify fractional expressions?
5. How do you evaluate composite functions like those involving square roots and absolute values?

**Tip:** Always check for domain restrictions when dealing with square roots and denominators to avoid undefined expressions.

Solve the given functions and evaluate at specified points.

Learn how to solve various functions involving square roots, absolute values, quadratic equations, and rational functions. The solutions break down key steps in simplifying and evaluating these functions. Suitable for students in Grades 9-12.

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