Name:_______________________ Date assigned:______________ Band:________Precalculus | Packer Collegiate InstituteRational Functions #2Section 1: What are the equations for these functions?You may keep your equations with both the numerator and denominator factored.A.

B.

C.

D.

E.

A.

B.

C.

D.

E.

Section 2: Algebraic stuff1. Rewrite your answer for D where the numerator and denominator are not factored, but expanded out.

2. Rewrite your answer for E in the same way.

Here is an interesting thing to note: a complicated algebraic equation can yield a very simple looking graph.3. (a) Write an equation for a function that is a horizontal line with a constant height of 3 but with a hole at

(b) The same as part (a) but with holes at and .

4.

Write an equation for a graph that has x intercepts at and , and a hole at .

5.

Write an equation for a graph that looks like the parabola , but has holes at and .

6.

We know, from the do now, that is a simple example of a graph with a vertical asymptote at . Do you think will have two vertical asymptotes? Why or why not? (Hint: Think about what happens when you multiply two functions together! Think about all the graphing multiplication we did!)

Now graph on your graphing calculator to see if your conjecture was correct.

(b) How do we know thatwill not have any x-intercepts?

(c) Come up with the equation for a function with two vertical asymptotes, at and .

(d) Okay, again, but now with vertical asymptotes at and , and a hole at .

7. (a) Challenge: Can you find the equation of a graph with x-intercepts at and , and a vertical asymptote at .

(b) Challenge: Can you find the equation of a graph with x-intercepts at and , a vertical asymptote at , and a hole at ?

Section 3: Taking Things Further Come Up With Your Own Problem Okay, youve seen a bunch of problems. What weve been doing is building up equations by multiplying things in special ways. What youre going to do is come up with your own problem, and then your own solution. Youve seen examples of various types of problems in Section 1 and Section 2. You should come up with a problem that involves both vertical asymptotes and holes. Heres the goal: Tomorrow youre going to be paired with someone, and your goal is to teach them what they missed. And youre going to do that by walking them through some of our insights, but also by walking them through your sample problem, and your solution!

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