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Copy HW in your planner.Copy HW in your planner.Text p.266 #4-34 even & #38Text p.266 #4-34 even & #38
In your notebook, explain in your own words the meaning In your notebook, explain in your own words the meaning of a function. What do functions consist of? How are of a function. What do functions consist of? How are functions different from equations?functions different from equations?
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Objective
SWBAT use function notation and graph functions
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Section 4.7 “Section 4.7 “Graph Linear FunctionsGraph Linear Functions””
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 FunctionsWhat 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 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) make a table by substituting into the make a table by substituting into the function. function.
(2) (2) plot the points from your table and connect plot the points from your table and connect the points with a line. the points with a line.
(3) (3) identify the domain and range, (if restricted)identify the domain and range, (if restricted)
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Graph 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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Graph a Function1122Graph the functionGraph the function f(x)f(x)
== – – xx + 4+ 4 with domainwith domain x x ≥≥ 0.0.
Then identify the range of the functionThen identify the range of the function..
STEP 1Make a table.
x 0 2 4 6 8
y 4 3 2 1 0
STEP 2
Connect the points with a ray because the domain is restricted.
Plot the points.
STEP 3Identify 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.
42
1)( xxf
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Family of FunctionsFamily of Functionsis a group of functions with similar characteristics. For example, functions that have the form f(x) = mx + b f(x) = mx + b constitutes the family of linear functions.constitutes the family of linear functions.
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Parent Linear FunctionParent Linear Function
The most basic linear function in the family of all linear functions is called the PARENT LINEAR FUNCTION which is:
f(x) = xf(x) = xxx -5-5 -2-2 00 11 33
f(x)f(x) -5-5 -2-2 00 11 33
f(x) = x
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Compare graphs with the graph f(x) = x.Compare graphs with the graph f(x) = x. Graph the function g(x) = x + 3, then compare it to Graph the function g(x) = x + 3, then compare it to
the parent function f(x) = x. the parent function f(x) = x.
x f(x)
-5 -2
-2 1
0 3
1 4
3 6
f(x) = xf(x) = xf(x) = x
x f(x)
-5 -5
-2 -2
0 0
1 1
3 3
g(x) = x + 3g(x) = x + 3g(x) = x + 3
The graphs of g(x) and f(x) have the same slope of 1.
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Compare graphs with the graph f(x) = x.Compare graphs with the graph f(x) = x. Graph the function h(x) = 2x, then compare it to the Graph the function h(x) = 2x, then compare it to the
parent function f(x) = x. parent function f(x) = x.
x f(x)
-3 -6
-2 -4
0 0
2 4
3 6
f(x) = xf(x) = xf(x) = x
x f(x)
-5 -5
-2 -2
0 0
1 1
3 3
h(x) = 2xh(x) = 2xh(x) = 2x
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.
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Real-Life FunctionsReal-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.
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Homework
Text p.266 #4-34 even & #38