92 direct and inverse variation graphs

9­2 direct and inverse variation graphs
Objectives:
• To graph direct variation.
• To graph inverse variation.
• To graph translations of inverse variations.
direct variation equations:
These equations follow the form
where k is
both the constant of variation and the slope. The y­intercept in a
direct variation graph is always (0, 0).
EX 1:
Key Features of Direct Variation Graphs:
• The graph is always a line.
• The constant k is also the slope.
• The line always passes through the origin.
practice problems:
Graph the following direct variation equations:

inverse variation equations:
These equations don’t follow any form we’ve seen before.
They are a new “family” of graphs.
EX 2:
>
Key Features of Inverse Variation Graphs:
>
• The graph always has two asymptotes.
One asymptote is horizontal ( ).
>
One asymptote is vertical ( ).
• The graph always has two symmetric branches.
>
graphing inverse variation “parents”:
1) Sketch and label both asymptotes:
and
2) Make an x/y table by choosing both whole number and fractional values that
work “nicely” with the numerator.
3) Plot the points in the table (for both branches) and connect the points.
Practice Problems:
Graph and sketch the following inverse variation equations:
Start with √k in the middle.
4.
Then choose two numbers
smaller and two numbers
larger than √k that work
nicely with k.

5.
Start with √k in the middle.
Then choose two numbers
smaller and two numbers
larger than √k that work
nicely with k.
Make sure you are creating
the table for both branches.
6.
the affect of
on inverse variation graphs:

describing translations:
Remember:
" x lies, y tells the truth"!
graphing inverse variation translations (“children”):
1) Identify the “parent” function and create the “parent” table.
2) Describe the shift. (Remember: “x lies, y tells the truth”)
3) Sketch and label the asymptotes based on the shift information.
4) Expand the parent table according to the shift description.
5) Plot the points in the table (for both branches) and connect the points.
EX 3:
Shift Description: ___________________________
Asymptotes:
____________ & ____________

Practice Problems:
Shift Description: ___________________________
7.
Asymptotes:
____________ & ____________
Practice Problems:
Shift Description: ___________________________
8.
Asymptotes:
____________ & ____________

tonight’s homework:
p. 488 #1, 3, 4, 8 ­ 10, 12, 14, 15, 19, 22 ­ 24, 34, 36, 37, 40
HOMEWORK TIPS:
USE GRAPH PAPER!!!
#4 ­ 9: 1. Graph both functions
2. Describe how the graphs are similar.
3. Describe how the graphs are different.
#10 & 12: 1. Enter the weight equation into Y1.
2. Enter the given weight into Y2.
3. Adjust the [ WINDOW ] to see where they intersect.
4. [ 2 nd ] [ TRACE ] 5:intersect
#34, 36 & 37
1. Solve each equation for y.
2. State whether you have direct, inverse or neither variation.
3. Graph the equation.