f(x)=(x^2+3x+2)/(x-1)

Question

GIVEN: f(x)=(x^2+3x+2)/(x-1) 

domain: 

vertical asymptote

holes 

horizontal asymptote 

x-intercept 

y-intercept

graph the function

Answer 1

The domain is all values of x for which f(x) is defined. For what value of x is this function undefined?

 

The vertical asymptote of a rational function occurs where the denominator equals 0.

 

To find the horizontal asymptote, compare the leading terms in the numerator and denominator. Since the numerator is of higher degree than the denominator, then this function has no horizontal asymptote because as x gets larger and larger, this function will tend towards infinity, or grow without bound.

 

The x-intercept occurs where y = 0

 

The y-intercept occurs where x = 0

 

You can use all of the above information to help you sketch the graph of f(x)

 

This function will also have a slant (or oblique) asymptote because the numerator is exactly one degree higher than the denominator. You can use long division of polynomials to determine the slant asymptote. It is possible that there may be a hole in the graph when you perform this operation.