I can help you interpret and solve the math problems in this image. Let’s analyze each question step by step.

The base function is $f(x) = 3x + 5$, and you are asked to describe how the graph of $g(x)$ changes compared to $f(x)$.

Detailed Explanation for Each Problem:

1. 15. $g(x) = (3x + 5) + 8$

   • This adds 8 to the y-values of $f(x)$, so the graph shifts 8 units up.

2. 16. $g(x) = (3x + 5) - 4$

   • Subtracting 4 decreases the y-values, shifting the graph 4 units down.

3. 17. $g(x) = 3(x + 5)$

   • Replacing $x$ with $x + 5$ shifts the graph 5 units to the left.

4. 18. $g(x) = 3(x - 1) + 5$

   • Replacing $x$ with $x - 1$ shifts the graph 1 unit to the right, and the $+5$ keeps the y-intercept constant.

5. 19. $g(x) = 3(0.1x) + 5$

   • Multiplying $x$ by $0.1$ compresses the graph horizontally by a factor of 10.

6. 20. $g(x) = 5(3x + 5)$

   • Multiplying the entire equation by 5 increases the slope and stretches the graph vertically by a factor of 5.

7. 21. $g(x) = 3(2x) + 5$

   • Replacing $x$ with $2x$ compresses the graph horizontally by a factor of 2.

8. 22. $g(x) = 8(3x + 5)$

   • Multiplying the entire equation by 8 increases the slope further and stretches the graph vertically by a factor of 8.

If you would like, I can expand on any of these explanations or solve additional related problems!

Follow-up Questions:

1. What are the effects of modifying the slope in $f(x) = mx + b$?
2. How does adding/subtracting constants outside $f(x)$ affect the graph?
3. How does replacing $x$ with $ax$ change the graph’s shape?
4. What is the difference between horizontal and vertical transformations?
5. Can these transformations be combined to create more complex changes?

Tip: Always plot key points like the y-intercept and a few other values to visualize transformations accurately.