How to find the x intercept of a rational function?
Understand the Problem
The question is asking us to identify the x-intercept of a rational function, which involves determining the value of x when the function's output (y) is equal to zero. This typically requires setting the numerator of the rational function to zero and solving for x.
Answer
Solve $P(x) = 0$
Answer for screen readers
The final answer involves solving the equation $P(x) = 0$
Steps to Solve
- Set the numerator equal to zero
For a rational function in the form $f(x) = \frac{P(x)}{Q(x)}$, the x-intercepts occur when the numerator $P(x)$ is equal to zero. This is because a rational function equals zero when its numerator is zero (and the denominator is not zero).
Set $P(x) = 0$
- Solve for x
Solve the equation obtained from setting the numerator equal to zero. This will give the x-values where the function intersects the x-axis.
Find the solutions to $P(x) = 0$
The final answer involves solving the equation $P(x) = 0$
More Information
The x-intercepts of a rational function occur where the value of the function is zero, which happens when the numerator of the function is zero (provided the denominator is not zero).
Tips
A common mistake is to forget to check if the value of x also makes the denominator zero. If it does, then that value of x is not an x-intercept but a point where the function is undefined.