The graph shown in the image is of an absolute value function $f(x)$, which appears to form a "V" shape. Let's break down the questions:

Part (a): Find the y-intercept

• The y-intercept occurs when $x = 0$. From the graph, we can see that when $x = 0$, the value of $y = -5$.
• Therefore, the y-intercept is $(0, -5)$.

Part (b): Find $f(-2)$

• To find $f(-2)$, look at where $x = -2$ on the graph.
• From the graph, when $x = -2$, the corresponding value of $y$ is $y = -1$.
• Therefore, $f(-2) = -1$.

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:

1. What is the vertex of the absolute value function, and how is it found?
2. How can you write the equation of the absolute value function based on this graph?
3. How would you find the x-intercepts of this function?
4. Can you explain how the slope changes on either side of the vertex?
5. How does the transformation of a basic absolute value function affect its graph?

Tip: The absolute value function typically takes the form $f(x) = a|x - h| + k$, where $(h, k)$ is the vertex, and $a$ affects the steepness of the V-shape.