Let's interpret the graph based on the given description and find approximate values of the function $f(x)$ for the specified points.

(a) $f(-5)$

From the description, we know that the first part of the graph is linear and crosses the x-axis at $x = -5$. This means that: $f(-5) = 0$

(b) $f(5)$

At $x = 5$, the function has two distinct parts. The first part ends at the open point $(5, 10)$, meaning that the value of $f(5)$ is not defined as 10 due to the open point. The second part begins at the closed point $(5, -15)$, meaning: $f(5) = -15$

(c) $f(15)$

The second part of the curve passes through the point $(15, 15)$, so: $f(15) = 15$

(d) $\frac{f(15) - f(5)}{15 - 5}$

Now, we calculate the difference quotient: $\frac{f(15) - f(5)}{15 - 5} = \frac{15 - (-15)}{15 - 5} = \frac{15 + 15}{10} = \frac{30}{10} = 3$

Final Answers:

• (a) $f(-5) = 0$
• (b) $f(5) = -15$
• (c) $f(15) = 15$
• (d) $\frac{f(15) - f(5)}{15 - 5} = 3$

Would you like more details on any of these steps or have any questions?

Here are 5 relative questions that expand on this topic:

1. What is the significance of an open point on a graph in relation to function values?
2. How would you determine if a function is continuous at a given point?
3. Can you explain what the difference quotient represents in calculus?
4. How can you find the slope of a line given two points on the graph?
5. How does the graph of a function help determine limits at particular points?

Tip: When interpreting graphs, always pay attention to open and closed points, as they indicate whether the function is defined at those values.