Answer:
- evaluate f(0)
- there will be 0 y-intercepts if f(0) is undefined, 1 otherwise.
Explanation:
You want to know how to determine the y-intercepts of a rational function, and their possible number.
Rational function
A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):
f(x) = p(x)/q(x)
As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...
f(0) = p(0)/q(0)
The values of p(0) and q(0) are simply the constant terms in those respective functions.
The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.
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