Let's analyze the problem shown in the image.

Problem Overview:

You are asked to use the graph provided to answer the following:

1. Determine the x-intercept(s), if any.
2. Determine the y-intercept(s), if any.

The question also asks you to choose the correct statement regarding the x-intercepts from the following options:

• (A) The x-intercept(s) are $\ldots$ (and you need to select the correct value).
• (B) There is no x-intercept.

Analyzing the Graph:

• X-Intercept(s): The x-intercepts are the points where the graph crosses the x-axis (i.e., where $y = 0$).

  • Looking at the graph, it appears that the graph does not cross the x-axis. Therefore, there are no x-intercepts.

• Y-Intercept(s): The y-intercepts are the points where the graph crosses the y-axis (i.e., where $x = 0$).

  • It seems the graph crosses the y-axis at $y = -1$. So, the y-intercept is $(0, -1)$.

Answer:

For the x-intercept:

• There is no x-intercept. This corresponds to option (B).

For the y-intercept:

• The y-intercept is $(0, -1)$.

Would you like any more details or further clarifications on this?

Additional Questions:

1. What are the steps to find the x-intercept if a graph does cross the x-axis?
2. How do you determine the y-intercept algebraically from an equation?
3. What are some common scenarios where a graph might have no x-intercepts?
4. Can a graph have more than one x-intercept? If so, how would you identify them?
5. How would you calculate intercepts if given an equation instead of a graph?

Tip:

When determining intercepts, always check where the graph touches or crosses the respective axis. This helps ensure you correctly identify if an intercept exists or not.