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Let's solve the given problems by finding the **x-intercepts** and **y-intercepts** of the functions.

### 1. \( f(x) = \frac{x - 25}{x - 5} \)

#### **X-Intercept:**
To find the **x-intercept**, set \( f(x) = 0 \).

\[
\frac{x - 25}{x - 5} = 0
\]

This happens when the numerator is 0:

\[
x - 25 = 0
\]

So, \( x = 25 \).

Thus, the x-intercept is at \( (25, 0) \).

#### **Y-Intercept:**
To find the **y-intercept**, set \( x = 0 \) and solve for \( f(x) \).

\[
f(0) = \frac{0 - 25}{0 - 5} = \frac{-25}{-5} = 5
\]

Thus, the y-intercept is at \( (0, 5) \).

### 2. \( f(x) = \frac{2x + 3}{x - 3} \)

#### **X-Intercept:**
Set \( f(x) = 0 \):

\[
\frac{2x + 3}{x - 3} = 0
\]

This occurs when the numerator is zero:

\[
2x + 3 = 0
\]

Solving for \( x \):

\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]

Thus, the x-intercept is at \( \left( -\frac{3}{2}, 0 \right) \).

#### **Y-Intercept:**
Set \( x = 0 \) to find the y-intercept:

\[
f(0) = \frac{2(0) + 3}{0 - 3} = \frac{3}{-3} = -1
\]

Thus, the y-intercept is at \( (0, -1) \).

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Would you like further explanation or additional details?

Here are 5 related questions for practice:
1. How do you find the vertical asymptote of these rational functions?
2. What happens if the denominator equals zero in a rational function?
3. Can you find the domain of each function?
4. How do you determine the horizontal asymptote of a rational function?
5. What is the significance of finding x- and y-intercepts in graphing functions?

**Tip:** When dealing with rational functions, always check for undefined points by setting the denominator equal to zero to find vertical asymptotes!

Find the x and y-intercepts of the following functions: 1. f(x) = (x - 25) / (x - 5) 2. f(x) = (2x + 3) / (x - 3)

This page shows how to find the x and y-intercepts of rational functions like f(x) = (x - 25) / (x - 5) and f(x) = (2x + 3) / (x - 3). Learn the step-by-step process for solving these types of algebraic problems. Suitable for students in Grades 9-12.

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