do now 6/11/10
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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. - PowerPoint PPT PresentationTRANSCRIPT
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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?
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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
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ObjectiveObjective
SWBAT use function notation. SWBAT use function notation.
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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’
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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
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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
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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)).
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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
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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
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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
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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.
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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.
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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.
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HomeworkHomework
Text p. 429, #12-28 evensText p. 429, #12-28 evens