https://file.aiquickdraw.com/mathbot/file/172556613738878x57ga9.jpg

I have opened the image, which shows multiple mathematical problems related to function evaluation, using graphs, equations, and tables.

Let's break down each problem:

1. **\( f(3) \)**: We are asked to evaluate \( f(3) \). The value of \( f(x) \) can be found by using the graph provided. We look for the point on the graph where \( x = 3 \), and find the corresponding \( y \)-value.

2. **Find \( x \) when \( f(x) = 4 \)**: This requires finding when the \( y \)-value on the graph equals 4 and determining the corresponding \( x \)-value.

3. **\( g(-3) \)**: For the function \( g(x) \), the values are given in the table. We look up \( g(-3) \) in the table.

4. **Find \( x \) when \( g(x) = 82 \)**: We need to find the value of \( x \) that makes \( g(x) = 82 \) in the table.

5. **\( h(16) \)**: The function \( h(x) \) is given by a formula, so we substitute \( x = 16 \) into \( h(x) = 3x - 23 \) to find the value.

6. **Find \( x \) when \( h(x) = 74 \)**: This requires solving the equation \( 3x - 23 = 74 \) for \( x \).

7. **\( p(74) \)**: Using the table, find \( p(74) \).

8. **Find \( t \) when \( p(t) = 12 \)**: This involves locating when the value of \( p(t) \) equals 12 in the table.

I'll now calculate these values.Here are the results for the given problems:

1. **\( f(3) = 2 \)** (from the graph).
2. **\( x = 5 \)** when \( f(x) = 4 \) (from the graph).
3. **\( g(-3) = 9 \)** (from the table).
4. **\( x = 50 \)** when \( g(x) = 82 \) (from the table).
5. **\( h(16) = 25 \)** (calculated from \( h(x) = 3x - 23 \)).
6. **\( x = \frac{97}{3} \approx 32.33 \)** when \( h(x) = 74 \) (solved from the equation \( h(x) = 3x - 23 \)).
7. **\( p(74) = 58 \)** (from the table).
8. **\( t = 16 \)** when \( p(t) = 12 \) (from the table).

Would you like more details on any of these steps?

Here are some related questions to think about:
1. How would you interpret the behavior of \( f(x) \) as \( x \) increases?
2. What kind of function might describe \( g(x) \) based on the table values?
3. How would you solve for \( h(x) = 100 \)?
4. If the graph of \( f(x) \) were extended, what would be the next logical value for \( f(x) \)?
5. What is the slope of the function \( h(x) \)?

**Tip**: When analyzing functions graphically, always double-check for turning points, as they can sometimes indicate maximum or minimum values.

Evaluate different functions using graphs, equations, and tables, including finding function values and solving equations.

Learn how to evaluate functions using graphs, solve equations, and interpret tables with this comprehensive guide. This problem includes function evaluation at specific points, solving for unknowns, and understanding linear equations. Perfect for students in Grades 8-10.

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