Name:_______________________ Date assigned:______________ Band:________Precalculus | Packer Collegiate InstituteRational Functions #1Warm Up: Multiplying Functions Together! Togethes!!!We are graphically going to multiply two functions together.

and .

Let .To get us primed, find and

Now do this for all the points! And for all the glory!!!

Section 1: Graphically Multiplying Functions Together

Do the same. Multiply the first two functions graphed to find the product of those functions. Do not do it algebraically.Problem 1:

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:

Section 2: Dividing FunctionsDividing two functions is slightly harder to do graphically. Remember that order matters for division! Try it! First, find

Problem 1:

Problem 2:

Problem 3:[footnoteRef:1] [1: Careful! Remember the Greatest Sin of Mathematics! Thou shalt not divide by.]

Problem 4:

Id like for you to check your final graph by filling in this very special table of values

In order to do that:

-3-2-100.50.90.9911.011.11.523

If you need to modify your graph based on the table of values, please do so.Follow Up! When we divide functions, we see crazy/unexpected things happen when [continue this sentence, and explain why the crazy things happen]

Problem 5: Challenge!

Section 3: ObservationsMultiplying Functions1. When multiplying functions, when one part of a function doesnt exist (e.g. a hole, a chunk of the function is missing), what happens to the product function at those values?

2. When multiplying functions, when one function has an x-intercept (and the other function exists), what is true about the product function?

3. When multiplying functions, when one function has a constant height of 1, how does that affect the product function?

Dividing Functions4. When dividing functions, we have a problem with dividing by zero. When the denominator of a function is zero, what possible things can happen in the quotient function at those values?

5. When dividing functions, when is the quotient function going to hit the x-axis? How do you know?

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