https://file.aiquickdraw.com/mathbot/file/1726785080129htwbx6dy.jpg

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### Problem 5:
Given \( g(x) = -7x + 4 \), find the following:
- a) \( g(-5) \)
- b) \( g(2) \)
- c) \( g(-1) \)
- d) \( g(0) \)

1. **\( g(-5) \)**:
   \[
   g(-5) = -7(-5) + 4 = 35 + 4 = 39
   \]
   
2. **\( g(2) \)**:
   \[
   g(2) = -7(2) + 4 = -14 + 4 = -10
   \]

3. **\( g(-1) \)**:
   \[
   g(-1) = -7(-1) + 4 = 7 + 4 = 11
   \]

4. **\( g(0) \)**:
   \[
   g(0) = -7(0) + 4 = 0 + 4 = 4
   \]

### Problem 6:
Given \( f(x) = 3x^2 - 1 \), find the following:
- a) \( f(9) \)
- b) \( f(-2) \)
- c) \( f(5) \)
- d) \( f(0) \)

1. **\( f(9) \)**:
   \[
   f(9) = 3(9^2) - 1 = 3(81) - 1 = 243 - 1 = 242
   \]

2. **\( f(-2) \)**:
   \[
   f(-2) = 3((-2)^2) - 1 = 3(4) - 1 = 12 - 1 = 11
   \]

3. **\( f(5) \)**:
   \[
   f(5) = 3(5^2) - 1 = 3(25) - 1 = 75 - 1 = 74
   \]

4. **\( f(0) \)**:
   \[
   f(0) = 3(0^2) - 1 = 0 - 1 = -1
   \]

### Problem 7:
Given \( g(x) = -4x^2 - 3x - 7 \), find the following:
- a) \( g(-4) \)
- b) \( g(-1) \)
- c) \( g(0) \)
- d) \( g(3) \)

1. **\( g(-4) \)**:
   \[
   g(-4) = -4(-4)^2 - 3(-4) - 7 = -4(16) + 12 - 7 = -64 + 12 - 7 = -59
   \]

2. **\( g(-1) \)**:
   \[
   g(-1) = -4(-1)^2 - 3(-1) - 7 = -4(1) + 3 - 7 = -4 + 3 - 7 = -8
   \]

3. **\( g(0) \)**:
   \[
   g(0) = -4(0)^2 - 3(0) - 7 = -7
   \]

4. **\( g(3) \)**:
   \[
   g(3) = -4(3^2) - 3(3) - 7 = -4(9) - 9 - 7 = -36 - 9 - 7 = -52
   \]

### Problem 8:
Given \( f(x) = x^2 - 2x \), find the following:
- a) \( f(-5) \)
- b) \( f(2) \)
- c) \( f(-8) \)
- d) \( f(1) \)

1. **\( f(-5) \)**:
   \[
   f(-5) = (-5)^2 - 2(-5) = 25 + 10 = 35
   \]

2. **\( f(2) \)**:
   \[
   f(2) = (2)^2 - 2(2) = 4 - 4 = 0
   \]

3. **\( f(-8) \)**:
   \[
   f(-8) = (-8)^2 - 2(-8) = 64 + 16 = 80
   \]

4. **\( f(1) \)**:
   \[
   f(1) = (1)^2 - 2(1) = 1 - 2 = -1
   \]

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Let me know if you need further details or clarifications on any of the steps.

Here are five related questions:
1. How do you find the value of a function at a given point?
2. What is the significance of the coefficients in linear functions?
3. How does the degree of a polynomial function affect its graph?
4. How can you identify whether a function is quadratic or linear by looking at the equation?
5. What does it mean if \( f(0) \) or \( g(0) \) gives a non-zero result?

**Tip:** For any quadratic function \( ax^2 + bx + c \), the vertex form can help you quickly identify the minimum or maximum value of the function.

Problems involving evaluating functions like g(x) = -7x + 4 and f(x) = 3x^2 - 1 at specific values such as x = -5, 2, -1, and 0.

Solve algebra problems involving the evaluation of linear and quadratic functions at specific points. Problems include evaluating functions such as g(x) = -7x + 4 and f(x) = 3x^2 - 1, providing step-by-step solutions.

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