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Do Now 6/11/10

Do Now 6/11/10. Take out HW from last night. Text p. 422, #8-22 even, #15 & #21 Copy HW in your planner. Text p. 429, #12-28 evens Quiz sections 8.6 & 8.7 Tuesday. Chapter 8 Test Wednesday.

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Do Now 6/11/10

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  1. Do Now 6/11/10 • Take out HW from last night. • Text p. 422, #8-22 even, #15 & #21 • Copy HW in your planner. • Text p. 429, #12-28 evens • Quiz sections 8.6 & 8.7 Tuesday. • 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?

  2. 8) y = -3x + 5 10) y = 13x – 8 12) y = 3x + 1 14) y = -2x + 3 15) y = 2x + 9 16) y = -5/4x – 6 18) y = 2x + 4 20) y = -8x – 2 21) y = -1/3x + 6 22) y = -x – 5 Homework Text p. 422, #8-22 even, #15 & #21

  3. Objective • SWBAT use function notation.

  4. 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. 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

  5. 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

  6. 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

  7. 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)).

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

  9. Graph an Function Using the Slope-Intercept Form Graph the function f(x) = -2x + 2 y-axis 5 4 Write in slope-intercept form 3 2 1 slope y-intercept -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x-axis -1 Slope of -2 means: -2 OR -3 Slope of -2 means: -4 -5

  10. Graph an function Using the Slope-Intercept Form Graph the function g(x) = -3 + 2/3x. y-axis 5 4 Rewrite in slope-intercept form 3 2 1 slope y-intercept -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x-axis -1 Slope of 2/3 means: -2 OR -3 Slope of 2/3 means: -4 -5

  11. Graph a Function Graph the Function f(x) = 2x – 3 SOLUTION STEP2 STEP3 STEP1 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.

  12. The function isf(x) = 3x + 5. y2 – y1 17 – 5 12 m 3 = = = = x2 – x1 4 – 0 4 Write an equation for the linear function fwith the values f(0) = 5 andf(4) = 17. STEP1 Write f(0) = 5 as (0, 5) and f (4)= 17 as (4, 17). STEP2 Calculate the slope of the line that passes through(0, 5) and (4, 17). STEP3 Write an equation of the line. The linecrosses they-axis at(0, 5).So, they-intercept is5. y =mx + b Write slope-intercept form. y =3x + 5 Substitute 3 for mand 5 for b.

  13. 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.

  14. Homework • Text p. 429, #12-28 evens

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