Consider the function y=ax+b/cx+d, where a, b, c, d are constants and c doesnt equal to 0, find the axes intercept 

Given the function \( y = \frac{ax + b}{cx + d} \), where \( a \), \( b \), \( c \), and \( d \) are constants and \( c \neq 0 \), we need to find the intercepts with the axes.

### 1. **x-intercept:**
The x-intercept occurs when \( y = 0 \). 

Set the function equal to zero:
\[
0 = \frac{ax + b}{cx + d}
\]

For a fraction to be zero, the numerator must be zero:
\[
ax + b = 0
\]

Solve for \( x \):
\[
x = -\frac{b}{a}
\]
So, the x-intercept is at \( x = -\frac{b}{a} \).

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

Substitute \( x = 0 \) into the function:
\[
y = \frac{a(0) + b}{c(0) + d} = \frac{b}{d}
\]

So, the y-intercept is at \( y = \frac{b}{d} \).

### Summary:
- **x-intercept:** \( x = -\frac{b}{a} \), or the point \( \left(-\frac{b}{a}, 0\right) \)
- **y-intercept:** \( y = \frac{b}{d} \), or the point \( \left(0, \frac{b}{d}\right) \)

Would you like more details or have any further questions?

### Related Questions:
1. How do the values of \( a \), \( b \), \( c \), and \( d \) affect the shape of the graph?
2. What happens if \( a = 0 \) or \( b = 0 \)?
3. Can you find the vertical asymptote for this function?
4. How does the sign of \( c \) impact the graph?
5. What is the behavior of the function as \( x \) approaches infinity?

**Tip:** Always check for undefined points in rational functions by analyzing where the denominator equals zero.

Learn how to find the x-intercept and y-intercept of the rational function y=ax+b/cx+d. This problem covers key concepts in rational functions and intercepts, including detailed steps and examples. Suitable for high school students.

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