1. Direct Variation and Graphing Linear Functions

2. 4.6 Direct Variation
Direct Variation modeled by y = mx, book uses y = ax.
b = 0 in direct variation.
Constant of Variation: fancy word for slope in a direct variation equation.

3. Examples of Direct Variation
y = 2x, constant of variation is 2
y = ¾x, constant of variation is ¾

4. Examples: Determine if Direct Variation is Represented
Examples: Determine if Direct Variation is Represented. If so, Identify the Constant of Variation.
2x – 3y = 0
-x + y = 4
2x + y = 0
-5x + 4y = 20

5. Graphing Direct Variation
y = 2x
y = - ½x

6. Example 3

7. Extra Example 3

8. Example 4

9. Homework 4.6
Page 256: 3 – 8, 12 – 18 evens, 24 – 34 evens,

10. 4.7 Function Notation

11. 4.7 Graph Linear Functions
Function notation: y is replaced with f(x).
f(x) is read “f of x” f is NOT a variable.
y = 2x + 1 and f(x) = 2x + 1 are the same graph.

12. Evaluating a function Evaluate f(x) = 3x – 15 when x = -3.
Ignore f(x), just plug in -3 for x.
f(-3) = 3(-3) – 15
f(-3) = -24
Note: this represents the point (-3, -24) on the graph.

13. Examples Evaluate the function h(x) = -7x when x = 7.
Evaluate the function f(x) = 2x + 12 when x = -8

14. Finding an x-value
For the function f(x) = 2x – 10, find the value of x so that f(x) = 6.

15. Extra Example
For the function f(x) = -2x + 4, find the value of x so that f(x) = 16.

16. Graphing Functions
Change the f(x) back to y (if needed) and graph as normal.
Graph f(x) = x + 7
Compare to f(x) = x

17. Graph
f(x) = x + 3 h(x) = 2x Compare both to f(x) = x.

18. Example 5
A cable company charges new customers $40 for installation and $60 per month for its service. The cost to the customer is given by the function f(x) = 60x + 40 where x is the number of months of service. To attract new customers, the cable company reduces the installation fee to $5. A function for the cost with the reduced installation fee is g(x) = 60x + 5. Graph both functions. How is the graph of g related to the graph of f?

19. Review
What does f(x) mean?

20. Homework
Page 265: 4, 6, 12 – 34 evens, 42-44