Do Now 11/10/09 Copy HW in your planner.

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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?

Objective SWBAT use function notation and graph functions

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

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. -24 B. -6 C. -2 D. 8 f(-3) = 3(-3) – 15 Simplify f(-3) = -9 – 15 f(-3) = -24

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

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)).

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)

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

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.

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.

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)

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.

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.

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.

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