Zeros of Rational Functions
INTERCEPTS OF RATIONAL FUNCTIONS
A rational function will have a -intercept at , if the function is defined at zero. A rational function will not have a y-intercept if the function is not defined at zero.
Likewise, a rational function will have -intercepts at the inputs that cause the output to be zero. Since a fraction is only equal to zero when the numerator is zero, -intercepts can only occur when the numerator of the rational function is equal to zero.
EXAMPLE 10
Finding the Intercepts of a Rational Function
Solution
We can find the -intercept by evaluating the function at zero
The -intercepts will occur when the function is equal to zero:
This is zero when the numerator is zero.
The -intercept is , the -intercepts are and . See Figure 16.
Figure 16
Source: Rice University, https://openstax.org/books/college-algebra/pages/5-6-rational-functions
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