1. Do Now 11/10/09 Copy HW in your planner. 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? 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. f(x) = mx + b slope y-intercept x-coordinate 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 This is read as ‘f of x’

4. Linear Functions What is the value of the function f(x) = 3x – 15 when x = -3? A. -24 B. -6 C. -2 D. 8 f(-3) = 3(-3) – 15 Simplify f(-3) = -9 – 15 f(-3) = -24

5. 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 6 = 2x – 10 8 = x 8 = x Solve for x. When x = 6, f(x) = 8

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

7. Graphing a Function To graph 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 a Functionx-2012f(x)-7-5-31 STEP 1 SOLUTION Graph the Function f(x) = 2x – 3 STEP 2 Make a table by choosing a few values for x and then finding values for y. STEP 3 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.

9. Graph a Function12 Graph the function f(x) = – x + 4 with domain x ≥ 0. Then identify the range of the function. STEP 1 Make a table. x 02468 y43210 STEP 2 Connect the points with a ray because the domain is restricted. Plot the points. 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 f(x) = mx + b constitutes the family of linear 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 x-5-2013 f(x)-5-2013

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. Graph the function g(x) = x + 3, then compare it to the parent function f(x) = x. xf(x) -5-2 1 03 14 36 f(x) = x xf(x) -5 -2 00 11 33 g(x) = x + 3 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. Graph the function h(x) = 2x, then compare it to the parent function f(x) = x. xf(x) -3-6 -2-4 00 24 36 f(x) = x xf(x) -5 -2 00 11 33 h(x) = 2x 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