Let's break down the problem based on the graph you provided.

We are asked to use the graph of the function $g$ to answer several questions:

a. Vertical Intercept

The vertical intercept (or y-intercept) is where the graph crosses the y-axis, i.e., when $x = 0$.

From the graph:

• At $x = 0$, the function intersects the y-axis at approximately $y = 3$.

So, the vertical intercept is $(0, 3)$.

b. Horizontal Intercepts

The horizontal intercepts (or x-intercepts) occur where the graph crosses the x-axis, i.e., where $g(x) = 0$.

From the graph:

• The function crosses the x-axis at two points: approximately $x = -2$ and $x = 4$.

Thus, the horizontal intercepts are $(-2, 0)$ and $(4, 0)$.

c. Evaluate $g(3)$

To evaluate $g(3)$, we look at the point on the graph where $x = 3$.

From the graph:

• When $x = 3$, $g(3) \approx 2$.

So, $g(3) = 2$.

d. Solve $g(x) = -3$

To solve $g(x) = -3$, we need to find the x-value(s) where the function equals -3.

From the graph:

• The function reaches $g(x) = -3$ at approximately $x = -1$.

So, the solution to $g(x) = -3$ is $x = -1$.

Would you like more detailed explanations, or do you have any other questions?

Here are five related questions:

1. How would you determine the domain and range of the function based on the graph?
2. What is the maximum value of the function $g$, and at what point does it occur?
3. Can you describe the intervals where the function is increasing and decreasing?
4. How would you solve for $g(x) = 1$ using the graph?
5. What is the symmetry of the graph? Is the function even, odd, or neither?

Tip: When analyzing graphs, always start by identifying key features such as intercepts, maxima/minima, and behavior at infinity to gain insights into the function's properties.