The image shows a piecewise linear graph, and the problem asks to:

1. Evaluate $f(3)$.
2. Solve for $f(x) = 3$.

Part a: Evaluate $f(3)$

To evaluate $f(3)$, locate $x = 3$ on the x-axis, and find the corresponding y-coordinate from the graph. The point at $x = 3$ appears to have the coordinate $(3, 4)$, meaning $f(3) = 4$.

Part b: Solve $f(x) = 3$

For this part, we need to find the x-values where the function equals 3, i.e., find the points on the graph where the y-coordinate is 3.

By observing the graph, we see that $f(x) = 3$ occurs at two points:

• When $x = 2$ (as the line crosses $y = 3$ at this point),
• When $x = 4$ (as the line crosses $y = 3$ at this point).

Therefore, the solutions to $f(x) = 3$ are $x = 2$ and $x = 4$.

Would you like further clarification or details?

Here are five related questions to consider:

1. How can we determine the equation of each linear segment of the graph?
2. What is the domain and range of the function shown in the graph?
3. How can the slope of the line segments help in evaluating other points on the graph?
4. How would we solve for $f(x) = 5$ using the same graph?
5. Can this piecewise linear function be expressed as a formula for each interval?

Tip: For piecewise functions, always break down the graph into segments and use slopes and intercepts to simplify calculations.