### Home > APCALC > Chapter 1 > Lesson 1.3.2 > Problem 1-117

For each part below, give an example of a function with specified attributes. Provide a sketch of each function. Homework Help ✎

A function with a hole at

*x*= 3 and an asymptote at*x*= −1.Write a rational function with (

*x*− 3) in both the numerator and the denominator to make a hole at*x*= 3.Remember that vertical asymptotes are formed by zeros in the denominator.

A function with asymptotes at the

*y*-axis and*x*= 5 and a hole at*x*= −4.An asymptote at the

*x*axis is the same as having a vertical asymptote of*x*= 0.A function with an end-behavior function

*g*(*x*) = 3*x*− 1.Holes and vertical asymptotes do not affect end behavior. How can

*y*= 3*x*− 1 be altered so that it has a hole or vertical asymptote?Possible answer:

*y*= 3*x*− 1 + [answer to part (a)].