Inverse Variation Breakdown (pt. 2)

Inverse Variation Breakdown (pt. 2)

Let's finish with Key Features and Solving!

Key Feature: Domain

Domain: All X-Values!

Be comfortable with either answer (saying All Reals EXCEPT x=0 or intervals splitting at x=0)

BE CAREFUL if the graph has moved left or right, check the x-value skipped in desmos with x=#

Key Feature: Range

Range: All Y-Values!

Be prepared for either answer type (All Reals EXCEPT y=0 or intervals split at 0).

BE CAREFUL if the graph has moved up or down, check the y-value skipped in desmos with y=#

Multiple Choice

What X and Y values are LEFT OUT for this graph's domain and range?

• x=2, y=-5

• x=-2, y=-5

• x=-2, y=5

• nothing gets left out!

WEIRD!!

Since this graph was slid down and left, it has different values left out of the domain and range!

Key Feature: End Behavior

• Remember you have two ends (left and right) to explain

• Left side is x -> - infinity

• Right side is x -> +infinity

Multiple Choice

What happens to the Value of y as x approaches +∞?

• y approaches infinity

• y approaches 2

• y approaches -2

• y approaches -infinity

Key Feature: Rate of Change

Increasing: Going up;

Decreasing: Going down;

Increasing RATE: gets steeper;

Decreasing RATE: gets flatter.

ALWAYS look LEFT to RIGHT!

With Rate of Change...

Remember you'll have two parts of this!

Multiple Choice

Describe the rate of change for positive x-values of this equation:

 $y=-\frac{3}{x}$  

• Decreases at decreasing rate

• Decreases at increasing rate

• Increases at decreasing rate

• Increases at increasing rate

Multiple Choice

Describe the rate of change for negative x-values of this equation:

 $y=-\frac{3}{x}$  

• Decreases at decreasing rate

• Decreases at increasing rate

• Increases at decreasing rate

• Increases at increasing rate

Multiple Choice

Describe the rate of change for positive x-values of this equation:

 $y=\frac{7}{x}$  

• Decreases at decreasing rate

• Decreases at increasing rate

• Increases at decreasing rate

• Increases at increasing rate

Multiple Choice

Describe the rate of change for negative x-values of this equation:

 $y=\frac{7}{x}$  

• Decreases at decreasing rate

• Decreases at increasing rate

• Increases at decreasing rate

• Increases at increasing rate

Last Section: SOLVING!

By hand, graphs, and tables.

Solving with Tables

When the tables have matching points, they're intersecting!

Your answer is usually the X VALUE!

Solving with Graphs

You're looking for the intersection(s) and providing the x-values!

Multiple Select

Find the solution(s) for these tables.

• x=-8

• x=3

• y=12

• x=0

Solving by Hand

Multiply by x to get it out of the denominator;

divide by the y-value;

simplify!

Solving by Hand: FROM CONTEXT

The only other thing is if I give you a situation and you have to write the equation (like yesterday) THEN solve it with a new variable.

Multiple Choice

If friends rent a cabin together, and spend $42 each when 8 people attend, how much will it cost if 12 people attended?

• $28

• $4,032

• $63