### Home > CALC > 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.A function with asymptotes at the

*y*-axis and*x*= 5 and a hole at*x*= −4.A function with an end behavior function

*g*(*x*) = 3*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.

An asymptote at the *x* axis is the same as having a vertical asymptote of *x* = 0.

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)]