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in words explain how to determine the y intercepts of a rational function. be sure to include if theres a specific way to easily find the y intercept and the possible number of y intercepts

User ARA
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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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User YaBoyQuy
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