sections 3.4 & 3...s3h lesson 3.4 & 3.6 part 1 filled in notes.notebook extra example (like problems...

S3H lesson 3.4 & 3.6 part 1 filled in notes.notebook

Sections 3.4 & 3.6

Inverse Variation

AND

Beginning Graphing of

Rational Functions


Section 3.4

Inverse Variation


Direct Variation:

Example: Inverse Variation:

Example:


So how do we know if a function has direct variation or inverse variation?* 1st check for inverse variation by checking if xy=k. Then you

can write the y=k/x equation. If that doesn't work, check for

direct variation.

* To check for direct variation, see if y/x=k. Then you can

write the y=kx equation.

* If it's not direct or inverse variation, we just say it's neither.


*


* *


*

*


Then

*


Now let's get really crazy & add more variables!!


Extra example (like problems 17 & 19 on homework):

z varies directly with x and inversely with the product of y and w. When x = 10, y = 1, w = 2, z = 15.

What is z when x = 2, y = 3, and w = 1 ?

*


Be careful to use correct units!

n = bags of mulch

Let's just set up the equation for this problem.*


Section 3.6Rational Functions

& Their Graphs


(-1,-1)

(1, 1)

This is the most basic rational function:

This graph has asymptotes at x = 0 and y = 0. It is pretty easy to graph by just plotting a few points, but what do we do if we have more complicated rational functions to graph?


* *

*


So how do we find vertical asymptotes?


*

*

*And what are the holes?


So basically:If the leading term's power on the top is smaller than the leading term's power on the bottom, then the horizontal asymptote is _________.

If the leading term's power on the top is equal to the leading term's power on the bottom, then the horizontal asymptote is

___________________________________.

If the leading term's power on the top is more than the leading term's power on the bottom, then ___________________________.


**

*


Assignment:Section 3.4: prob. 8, 9, 11, 16, 17, 19

AND

Section 3.6: prob. 1-6 (for #1 & 2, just find points of discontinuity and intercepts),

& 10-17 (on these find all asymptotes, holes, and intercepts)

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sections 3.4 & 3...s3h lesson 3.4 & 3.6 part 1 filled in notes.notebook extra example (like problems...

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