1. Do Now 11/10/09 Copy HW in your planner.
Text p.266 #4-34 even & #38
In your notebook, explain in your own words the meaning of a function. What do functions consist of? How are functions different from equations?

2. Objective
SWBAT use function notation and graph functions

3. Section 4.7 “Graph Linear Functions”
Function Notation-
a linear function written in the form y = mx + b where y is written as a function f.
x-coordinate
f(x) = mx + b
This is read
as ‘f of x’
slope
y-intercept
f(x) is another name for y.
It means “the value of f at x.”
g(x) or h(x) can also be used to name functions

4. What is the value of the function f(x) = 3x – 15 when x = -3?
Linear Functions
What is the value of the function f(x) = 3x – 15 when x = -3?
A B C D. 8
f(-3) = 3(-3) – 15
Simplify
f(-3) = -9 – 15
f(-3) = -24

5. f(x) = 2x – 10 6 = 2x – 10 8 = x Linear Functions
For the function f(x) = 2x – 10, find the value of x so that f(x) = 6.
f(x) = 2x – 10
Substitute into the function
6 = 2x – 10
Solve for x.
8 = x
When x = 6, f(x) = 8

6. Domain and Range
Domain = values of ‘x’ for which the function is defined.
Range = the values of f(x) where ‘x’ is in the domain of the function f.
The graph of a function f is the set of all points (x, f(x)).

7. Graphing a Function To graph a function:
(1) make a table by substituting into the function.
(2) plot the points from your table and connect the points with a line.
(3) identify the domain and range, (if restricted)

8. Graph the Function f(x) = 2x – 3
Graph a Function
Graph the Function f(x) = 2x – 3
SOLUTION
STEP 2
STEP 3
STEP 1
Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.
The domain and range are not restricted therefore, you do not have to identify.
Make a table by choosing a few values for x and then finding values for y. x -2 -1 1 2
f(x) -7 -5 -3

9. Graph a Function 1 2 Graph the function f(x) = – x + 4
with domain x ≥ 0.
Then identify the range of the function.
STEP 1 x 2 4 6 8 y 3 1
Make a table.
STEP 2
Plot the points.
Connect the points with a ray
because the domain is restricted.
STEP 3
Identify the range. From the graph, you can see that all points have a y-coordinate of 4 or less, so the range of the function is y ≤ 4.

10. Family of Functions
is a group of functions with similar characteristics. For example, functions that have the form f(x) = mx + b constitutes the family of linear functions.

11. Parent Linear Function
The most basic linear function in the family of all linear functions is called the PARENT LINEAR FUNCTION which is:
f(x) = x
f(x) = x x -5 -2 1 3
f(x)

12. Compare graphs with the graph f(x) = x.
Graph the function g(x) = x + 3, then compare it to the parent function f(x) = x.
f(x) = x
g(x) = x + 3
g(x) = x + 3
f(x) = x x
f(x) -5 -2 1 3 x
f(x) -5 -2 1 3 4 6
The graphs of g(x) and f(x) have the same slope of 1.

13. Compare graphs with the graph f(x) = x.
Graph the function h(x) = 2x, then compare it to the parent function f(x) = x.
f(x) = x
h(x) = 2x
h(x) = 2x
f(x) = x x
f(x) -5 -2 1 3 x
f(x) -3 -6 -2 -4 2 4 3 6
The graphs of h(x) and f(x) both have a y-int of 0.
The slope of h(x) is 2 and therefore is steeper than f(x) with a slope of 1.

14. Real-Life Functions
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 ?
The graphs of both functions are shown. Both functions have a slope of 60, so they are parallel. The y-intercept of the graph of g is 35 less than the graph of f. So, the graph of g is a vertical translation of the graph of f.

15. Homework
Text p.266 #4-34 even & #38