Find the *x*- and *y*-intercepts for the function.

*f*(*x*) =

*x* + 5

*x*2 + 4

*x*-intercept

(*x*, *y*) =

*y*-intercept

(*x*, *y*) =

To find the *x*- and *y*-intercepts of the function:

\[ f(x) = \frac{x + 5}{x^2 + 4} \]

### 1. *x*-intercept:
The *x*-intercept occurs when \( f(x) = 0 \), or equivalently, when \( y = 0 \). This means we set the numerator equal to zero and solve for *x*.

\[
x + 5 = 0
\]
\[
x = -5
\]

So, the *x*-intercept is:

\[
(x, y) = (-5, 0)
\]

### 2. *y*-intercept:
The *y*-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the function:

\[
f(0) = \frac{0 + 5}{0^2 + 4} = \frac{5}{4}
\]

So, the *y*-intercept is:

\[
(x, y) = (0, \frac{5}{4})
\]

### Summary:
- **x-intercept**: \((-5, 0)\)
- **y-intercept**: \((0, \frac{5}{4})\)

Would you like more details or have any further questions?

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Here are 5 related questions:
1. How do you find intercepts for more complex functions?
2. Can a function have more than one *x*-intercept or *y*-intercept?
3. What happens if the numerator has no real solutions for the *x*-intercept?
4. How do you interpret intercepts graphically?
5. What if the denominator equals zero at a certain point?

**Tip**: Always check if the denominator is zero to avoid undefined values in rational functions!

Find the x- and y-intercepts for the function.

f(x) = (x + 5) / (x^2 + 4)

x-intercept
(x, y) = 

y-intercept
(x, y) = 

Learn how to find the x- and y-intercepts of the rational function (x + 5) / (x^2 + 4) with step-by-step solutions. This problem covers key concepts in algebra and rational functions, focusing on finding intercepts by solving for x and y. Ideal for students in Grades 9-11.

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