Do Now 6/11/10 Take out HW from last night. Take out HW from last night. Text p. 422, #8-22 even, #15 & #21 Text p. 422, #8-22 even, #15 & #21 Copy HW.

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Do Now 6/11/10 Take out HW from last night. Take out HW from last night. Text p. 422, #8-22 even, #15 & #21 Text p. 422, #8-22 even, #15 & #21 Copy HW in your planner. Copy HW in your planner. Text p. 429, #12-28 evens Text p. 429, #12-28 evens Quiz sections 8.6 & 8.7 Tuesday. Quiz sections 8.6 & 8.7 Tuesday. Chapter 8 Test Wednesday. Chapter 8 Test Wednesday. In your notebook, answer the following question. How would you graph the following equation, y= 3x + 4? How would you graph a function, f(x) = 3x + 4? In your notebook, answer the following question. How would you graph the following equation, y= 3x + 4? How would you graph a function, f(x) = 3x + 4?

Homework Text p. 422, #8-22 even, #15 & #21 8) y = -3x + 5 8) y = -3x ) y = 13x – 8 10) y = 13x – 8 12) y = 3x ) y = 3x ) y = -2x ) y = -2x ) y = 2x ) y = 2x ) y = -5/4x – 6 16) y = -5/4x – 6 18) y = 2x ) y = 2x ) y = -8x – 2 20) y = -8x – 2 21) y = -1/3x ) y = -1/3x ) y = -x – 5 22) y = -x – 5

Objective SWBAT use function notation. SWBAT use function notation.

Section 8.7 “Function Notation” 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’

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

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

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)).

Graphing a Function To graph a function: To graph a function: (1) rewrite the function in slope-intercept form. (1) rewrite the function in slope-intercept form. (2) plot the y-intercept. (2) plot the y-intercept. (3) use the slope starting at the y-intercept. (3) use the slope starting at the y-intercept. (4) draw a line through the points (4) draw a line through the points

y-axis x-axis Graph an Function Using the Slope-Intercept Form Graph the function f(x) = -2x + 2 Write in slope-intercept form slopey-intercept Slope of -2 means: -2 means: Slope of -2 means: -2 means: OR

y-axis x-axis Graph an function Using the Slope-Intercept Form Graph the function g(x) = /3x. Rewrite in slope-intercept form slopey-intercept Slope of 2/3 means: 2/3 means: Slope of 2/3 means: 2/3 means: OR

Graph a Function x-2012f(x) 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.

Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17. Calculate the slope of the line that passes through (0, 5) and (4, 17). Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17). STEP 1 x 2 – x 1 4 – 0 y 2 – y 1 = m = 17 – 5 = 4 12 = 3 STEP 2 y = mx + b Write slope-intercept form. y = 3x + 5 Substitute 3 for m and 5 for b. Write an equation of the line. The line crosses the y -axis at (0, 5). So, the y- intercept is 5. STEP 3 The function is f(x) = 3x + 5.

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. 429, #12-28 evens Text p. 429, #12-28 evens