https://file.aiquickdraw.com/mathbot/file/1726621031310vh76vyw6.jpg

Let's go through the questions based on the image you've provided:

### 1. Function Problems:
1. \( f(x) = 6x + 5 \)
   - \( f(2) = 6(2) + 5 = 12 + 5 = 17 \)
   - \( f(-2) = 6(-2) + 5 = -12 + 5 = -7 \)

2. \( g(x) = 3^x \)
   - \( g(4) = 3^4 = 81 \)
   - \( g(0) = 3^0 = 1 \)

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### 2. Graph-Based Questions:
The graph represents the distance traveled by a biker over time.

3. **How far away are they at 0.5 hours?**
   - From the graph, at \( t = 0.5 \) hours, the distance is about **5 miles**.

4. **How long does it take them to reach 2 miles away?**
   - From the graph, the biker reaches 2 miles at approximately **0.2 hours**.

5. **Which of the variables is represented by \( f(n) \)?**
   - This would be **B. Distance**, as the graph represents distance as a function of time.

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Would you like further details or explanations? Here are five follow-up questions for additional practice:

1. What is the slope of the line for the function \( f(x) = 6x + 5 \)?
2. What is \( g(3) \) if \( g(x) = 3^x \)?
3. At what time does the biker stop moving, according to the graph?
4. How far does the biker travel in the first hour?
5. How could you describe the relationship between time and distance in the graph?

**Tip:** When analyzing a graph, always look at the axis labels to understand what each variable represents!

Use the explicit function equations to find the indicated values. Use the graph to answer the questions about a biker's travel over time.

Solve linear and exponential function problems like f(x) = 6x + 5 and g(x) = 3^x. Use graph interpretation to find the distance traveled by a biker over time. Suitable for Grades 7-10 students.

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