Do Now 6/11/10Do Now 6/11/10Take out HW from last night.Take out HW from last night.

Text p. 422, #8-22 even, #15 & #21Text p. 422, #8-22 even, #15 & #21

Copy HW in your planner. Copy HW in your planner. Text p. 429, #12-28 evensText p. 429, #12-28 evensQuiz 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 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?following equation, y= 3x + 4? How would you graph a function, f(x) = 3x + 4?

HomeworkHomework Text p. 422, #8-22 even, #15 & #21 Text p. 422, #8-22 even, #15 & #21

8) y = -3x + 58) y = -3x + 5 10) y = 13x – 810) y = 13x – 8 12) y = 3x + 112) y = 3x + 1 14) y = -2x + 314) y = -2x + 3 15) y = 2x + 915) y = 2x + 9 16) y = -5/4x – 6 16) y = -5/4x – 6 18) y = 2x + 418) y = 2x + 4 20) y = -8x – 2 20) y = -8x – 2 21) y = -1/3x + 621) y = -1/3x + 6 22) y = -x – 5 22) y = -x – 5

ObjectiveObjective

SWBAT use function notation. SWBAT use function notation.

Section 8.7 “Section 8.7 “Function NotationFunction Notation””

Function Notation-Function Notation-a linear function written in the form a linear function written in the form y = mx + by = mx + b where y is written as a function where y is written as a function f.f.

f(x) = mx + bf(x) = mx + bslopeslope y-intercepty-intercept

x-coordinatex-coordinate

f(x) is another name for y.f(x) is another name for y.It means “the value of f at x.”It means “the value of f at x.”g(x) or h(x) can also be used to name functions g(x) or h(x) can also be used to name functions

This is read This is read as ‘f of x’as ‘f of x’

Linear FunctionsLinear Functions

What is the value of the function What is the value of the function f(x) = 3x – 15 when x = -3?f(x) = 3x – 15 when x = -3?

A. -24 B. -6 C. -2 D. 8A. -24 B. -6 C. -2 D. 8

f(f(-3-3) = 3() = 3(-3-3) – 15 ) – 15 Simplify

f(f(-3-3) = -9 – 15 ) = -9 – 15 f(f(-3-3) = -24 ) = -24

Linear FunctionsLinear Functions

For the function f(x) = 2x – 10, find the For the function f(x) = 2x – 10, find the value of value of xx so that f(x) = 6. so that f(x) = 6.

f(x)f(x) = 2x – 10 = 2x – 10 Substitute into the function

66 = 2x – 10 = 2x – 10

8 = x 8 = x Solve for x.

When x = 6, f(x) = 8When x = 6, f(x) = 8

Domain and RangeDomain and Range

DomainDomain = values of ‘x’ for which the function is = values of ‘x’ for which the function is defined.defined.

Range Range = the values of f(x) where ‘x’ is in the = the values of f(x) where ‘x’ is in the domain of the function domain of the function f. f.

The graph of a function The graph of a function f f is the set of all points is the set of all points (x, f(x)). (x, f(x)).

Graphing a FunctionGraphing a Function

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

11

22

33

44

55

00 11 22 33 44 55 66

y-axisy-axis

x-axisx-axis-6-6 -5-5 -4-4 -3-3 -2-2 -1-1

-5-5

-4-4

-3-3

-2-2

-1-1

Graph an Function Using the Slope-Intercept FormGraph an Function Using the Slope-Intercept Form

Graph the function Graph the function f(x) = -2x + 2 f(x) = -2x + 2

Write in slope-intercept formWrite in slope-intercept form

22)( xxf

slopeslope y-intercepty-intercept

Slope ofSlope of -2 means: -2 means: run

rise

1

2

Slope ofSlope of -2 means: -2 means: run

rise

1

2OROR

11

22

33

44

55

00 11 22 33 44 55 66

y-axisy-axis

x-axisx-axis-6-6 -5-5 -4-4 -3-3 -2-2 -1-1

-5-5

-4-4

-3-3

-2-2

-1-1

Graph an function Using the Slope-Intercept FormGraph an function Using the Slope-Intercept Form

Graph the function Graph the function g(x) = -3 + 2/3xg(x) = -3 + 2/3x..

xxg3

23)(

Rewrite in slope-intercept formRewrite in slope-intercept form

33

2)( xxg

slopeslope y-intercepty-intercept

Slope ofSlope of 2/3 2/3

means: means: run

rise

3

2

Slope ofSlope of 2/3 2/3

means: means: run

rise

3

2OROR

Graph a FunctionGraph a Function

32)( xxf

xx -2-2 -1-1 00 11 22

f(x)f(x) -7-7 -5-5 -3-3 -1-1 11

STEPSTEP 11

SOLUTION

Graph the Function Graph the Function f(x) = 2x – 3 f(x) = 2x – 3

STEPSTEP 22

Make a table by choosing a few values for x and then finding values for y.

STEPSTEP 33

Plot the points. Notice the points appear on a line. Connect the points drawing a line through them.

32)( xxf

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

x2 – x1 4 – 0y2 – y1=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 FunctionsReal-Life Functions

A cable company charges new customers $40 for A cable company charges new customers $40 for installation and $60 per month for its service. The cost to the installation and $60 per month for its service. The cost to the customer is given by the function customer is given by the function ff((xx) = 60) = 60x x +40 where +40 where x x is the is the number of months of service. To attract new customers, the number of months of service. To attract new customers, the cable company reduces the installation fee to $5. A function cable company reduces the installation fee to $5. A function for the cost with the reduced installation fee is for the cost with the reduced installation fee is gg((xx) = 60) = 60x x + 5. + 5. Graph both functions. How is the graph of Graph both functions. How is the graph of g g related to the related to the graph of graph of f f ??

The graphs of both functions are The graphs of both functions are shown. Both functions have a slope of shown. Both functions have a slope of 60, so they are parallel. The 60, so they are parallel. The yy-intercept -intercept of the graph of of the graph of g g is 35 less than the is 35 less than the graph of graph of ff. So, the graph of . So, the graph of g g is a is a vertical translation of the graph of vertical translation of the graph of f.f.

HomeworkHomework

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