8.7 Function Notation class.notebook
February 05, 2013
When you use an equation to represent a function it is often
convenient to give the function a name, such as
f or g. For instance,
the function y = x + 2 can be written in function notation as follows:
f(x) = x + 2
The symbol f(x), which replaces y, is read "f of x" and represents the
value of the function f at x. For instance, f (3) is the value of x when x =3
Let f (x) = 2x ­ 5. a. Find f(x) when x = ­3 b. Now find x when f(x) = 13 (These are different problems ­­­ asking to find different unknowns.
a. f (x) = 2x ­ 5
Write function
Substitute for x on both sides of the equation.
Simplify ­ Solve for x
b. f(x) = 2x ­5
Write function
Substitue for f(x) this time
Answer: When x = -3, f(x) = -11
Solve for x
x = 9, f(x) = 13
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8.7 Function Notation class.notebook
February 05, 2013
Graphing a Function
y
5
4
Graph the function 3
2
1
1. Rewrite the function as ­2
­1
0
­1
x
1
2
3
4
5
6
7
8
9
10
­2
­3
2. The y ­intercept is ­3 so plot the point (0,­3).
3. The slope is 5/6. Starting at (0,­3) plot another
point by moving up 5 units and over 6 units.
­4
­5
­6
4. Draw a line through the points.
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8.7 Function Notation class.notebook
February 05, 2013
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8.7 Function Notation class.notebook
February 05, 2013
Writing a Function
Write a linear function g given that g(0) =10 and g(4) = ­2.
Find the slope using the slope formula.
What are the coordinates of the points?
(0,10), (4,2)
Find the y­ intercept b of the function's graph.
y­intercept = 10
Write an equation in function form.
g(x) = ­3x + 10
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8.7 Function Notation class.notebook
February 05, 2013
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8.7 Function Notation class.notebook
February 05, 2013
You ride your bike at a speed of 12 miles per hour.
a Use function notation to write an equation giving the distance traveled as a function of time.
b. How long will it take you to travel 30 miles?
Solution
Let t be the elapsed time (in hours) since you started riding your bike,
and let d(t) be the distance traveled (in miles) at that time.
Write a model. Then use the model to write an equation.
Distance traveled = Speed of Bike *
Time
Find the value of t for which d(t) = 30
d(t) =
Write the function formula for distance.
Substitute for d(t)
Answer: It will take you 2.5 hours to travel 30 miles.
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8.7 Function Notation class.notebook
February 05, 2013
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