Let's analyze the graphs and determine the $x$- and $y$-intercepts for each of the given functions:

1. Graph 1:

• $x$-intercept(s): The graph touches the $x$-axis at approximately $x = 3$, so the $x$-intercept is $(3, 0)$.
• $y$-intercept: The graph crosses the $y$-axis at approximately $y = 2$, so the $y$-intercept is $(0, 2)$.

2. Graph 2:

• $x$-intercept(s): The graph crosses the $x$-axis at three points: $x = -3$, $x = -1$, and $x = 1$. So, the $x$-intercepts are $(-3, 0), (-1, 0), (1, 0)$.
• $y$-intercept: The graph crosses the $y$-axis at approximately $y = -1$, so the $y$-intercept is $(0, -1)$.

3. Graph 3:

• $x$-intercept(s): The graph does not touch or cross the $x$-axis, so there are no $x$-intercepts.
• $y$-intercept: The graph crosses the $y$-axis at approximately $y = 0$, so the $y$-intercept is $(0, 0)$.

4. Graph 4:

• $x$-intercept(s): The graph touches the $x$-axis at $x = -2$ and $x = 2$, so the $x$-intercepts are $(-2, 0), (2, 0)$.
• $y$-intercept: The graph crosses the $y$-axis at approximately $y = 4$, so the $y$-intercept is $(0, 4)$.

5. Graph 5:

• $x$-intercept(s): The graph crosses the $x$-axis at $x = -2$ and $x = 2$, so the $x$-intercepts are $(-2, 0), (2, 0)$.
• $y$-intercept: The graph crosses the $y$-axis at approximately $y = -1$, so the $y$-intercept is $(0, -1)$.

6. Graph 6:

• $x$-intercept(s): The graph does not touch or cross the $x$-axis, so there are no $x$-intercepts.
• $y$-intercept: The graph does not cross the $y$-axis, so there is no $y$-intercept.

Would you like further details or clarifications?

Here are five related questions to deepen your understanding:

1. How do you find the $x$- and $y$-intercepts algebraically from an equation?
2. Why do some graphs have no $x$- or $y$-intercepts?
3. How can symmetry of a graph help in identifying intercepts?
4. What are the characteristics of a function with multiple $x$-intercepts?
5. How do vertical and horizontal asymptotes affect the intercepts of a graph?

Tip: The $x$-intercept is found when $y = 0$, and the $y$-intercept is found when $x = 0$. Always substitute these values into the function to verify the intercepts algebraically.