High School Pre-Cal

Question

Which statement about the function below is true?

 

f(x)=(13x-7)÷ x+4




A.The function has a horizontal asymptote at f(x) = 13.

B.The function has a horizontal asymptote at f(x) = 4.

C.The function has a vertical asymptote at x = 13.

 

D.The function has a vertical asymptote at x = 4.

Answer 1

Hi Kenneth,

 

The answer is A because

 

As x gets VERY LARGE, you have 13 times a very large number divided by a very large number which basically equals 13

 

It also approaches 13 for when x becomes a VERY LARGE NEGATIVE number

 

It has a vertical asymptote at x =-4 but this isn't a choice

 

The vertical asymptote is based on what x cannot be equal to according to what would make the denominator = 0