1. Direct Variation
Direct Variation: y varies directly as x or y is directly proportional to x (y=kx) where k is the constant of proportionality or constant of variation
As x gets larger, y gets larger or as x gets smaller, y gets smaller
The graph of a direct variation equation is continuous for all values of x and passes through the origin

2. Inverse Variation
Inverse Variation: y varies inversely as x or y is inversely proportional to x
(y = (k/x) or xy = k) where k is the constant of proportionality or constant of variation
As x gets larger, y gets smaller or as x gets smaller, y gets larger
The graph of an inverse variation equation is NOT continuous for all x-values and does not have a y-intercept

3. Examples of Direct Variation
Real world examples of direct variation include:
Fruit sold by the pound
Distance traveled by a car over time
Characters printed from a computer per second
Circumference of a circle varies directly as the diameter
Wages varying directly to hours worked
Hours worked and paid
Distance and time
Itunes (amount of songs purchased and total amount spent)
Length of sides of a figure and perimeter of the figure

4. Examples of Inverse variation
Real world examples of inverse variation includes:
Trip to myrtle beach, the greater your car speed the less time it would take you to get there
If a rectangle has an area of 15 square units, then as the length increases the width decreases
Time it takes for ice to melt varies inversely with the temperature
Number of people eating pizza and number of pieces of pizza available per person

5. Examples
Example 1: If y varies directly as x and s=10 when y=9, then what is y when x=4?

6. Examples
When a bicycle is pedaled in a certain gear, it travels 16 meters for every 3 pedal revolutions. How many revolutions would be needed to travel 600 meter?
Use d=kr

7. Example
If y varies inversely as x and x=3 and y=9, then what is x when y=27?

8. Example
If y varies inversely as the square of x and y=20 when x=4, find y when x=5.

9. Graph Characteristics
Define by using your phone:
Discrete:
Continuous:
Discontinuous:
Increasing:
Decreasing:
Constant:

10. Actual Definitions Discrete: Data that can only take certain values
Ex: the number of students in a class (you cannot have half a student)
Not continuous data
Continuous: A function is continuous when its graph is unbroken
You can draw the function without lifting your pencil
Discontinuous: a graph that has a form of discontinuity
Types of discontinuity: holes, jump, asymptotes

11. Definitions continued…
Increasing: when the y-value increases as the x-value increases
Tends to go up
Decreasing: y-value decreases as the x-value decreases
Tends to go down
Constant: is a horizontal line
F(x)=k

12. Quiz Piecewise functions Compositions Go over:
Graphing
Go over:
Evaluating f(x)
A f(x) takes a value of x and applies the following:
Domain
Step 1) divide x by 3
Range
Step 2) subtract 7 from the result in Step 1
Increasing and decreasing
Now what steps would be need to describe the inverse function
Step 1) multiply x by 3
Practice: pg #1-4
Step 2) add 7 from the result in Step 1
Solving absolute value equations and inequalities
Inverses
Graph absolute values and create a piecewise from that
Direct and Inverse Variation