To find the intercepts of the given function:

$y = \frac{x^2 - 9}{x^2 - 16}$

1. X-intercepts: The x-intercepts occur where $y = 0$. To find them, set $y = 0$ in the equation and solve for $x$:

$0 = \frac{x^2 - 9}{x^2 - 16}$

For this to be true, the numerator must be 0, so:

$x^2 - 9 = 0$

Solving for $x$:

$x^2 = 9$

$x = \pm 3$

Thus, the x-intercepts are at $x = 3$ and $x = -3$. The corresponding points are $(3, 0)$ and $(-3, 0)$.

2. Y-intercept: The y-intercept occurs where $x = 0$. To find it, substitute $x = 0$ into the equation:

$y = \frac{0^2 - 9}{0^2 - 16} = \frac{-9}{-16} = \frac{9}{16}$

Thus, the y-intercept is $\left( 0, \frac{9}{16} \right)$.

Conclusion:

The intercepts are:

• X-intercepts: $(3, 0)$ and $(-3, 0)$
• Y-intercept: $\left( 0, \frac{9}{16} \right)$

Answer Choice: A. The intercept(s) are $(3, 0), (-3, 0), \left( 0, \frac{9}{16} \right)$.

Would you like more details or have any questions about this solution?

Here are five related questions to explore:

1. How do vertical asymptotes affect the intercepts of a rational function?
2. How do you find the domain and range of a rational function?
3. How can you determine if a rational function has a horizontal or oblique asymptote?
4. What is the significance of simplifying a rational function before finding intercepts?
5. How do you find the x-intercepts of a rational function that has no numerator?

Tip: To find intercepts of any function, always substitute 0 for the respective variable (x for y-intercepts and y for x-intercepts) and solve for the other variable.