section 2.1 what is a function?
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Section 2.1 What is a function?. Objectives: To understand functions and function notation. To review domain. To understand how to evaluate functions and piecewise functions. To understand the difference quotient. Functions. - PowerPoint PPT PresentationTRANSCRIPT
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Section 2.1What is a function?
Objectives:• To understand functions and function notation.• To review domain.• To understand how to evaluate functions and piecewise functions.• To understand the difference quotient.
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Functions
• A curve in the coordinate plane is the graph of a function if and only if no vertical line intersects the curve more than once.
• Vertical Line Test – when given a graph, use this to verify if the curve is a function
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Ex 1. Use the vertical line test to determine if the following graphs are functions.
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FunctionsA function is a relationship between two variables such
that each value of the first variable is paired with exactly one value of the second variable.
Function notation: f(x) = yf(2) means evaluate the given function when
x=2
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Ex 2. Given 2
1( )
1f x
x
Evaluate:
a)f(3)
b)f(-2)
c)f( )5
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Getting Information from a Graph
• The values of a function are represented by the height of its graph above the x-axis.
– So, we can read off the values of a function from its graph.
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Ex. 3 Find the Values of a Function from a Graph
The function T graphed here gives the temperature between noon and 6 P.M. at a certain weather station.
(a) Find T(1), T(3), and T(5).(b) Which is larger, T(2) or T(4)?
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Class Work
1)
a) Find f(50).
b) Find f(100).
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2.) Evaluate at the given values.
a)f(-2) b) f(4) c) f( ½ )
Class Work2( ) 3 5f x x x
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Piecewise Functions
A piecewise function is defined by different formulas on different parts of the domain.
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Ex 4. A cell phone plan costs $39 a month.• The plan includes 400 free minutes and charges
20¢ for each additional minute.• The monthly charges are a function of the
number of minutes used, given by
Find C(100), C(400), and C(480)
39 0 400( )
39 0.2( 400) 400
if xC x
x if x
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Class Work3. Evaluate the piecewise functions at the indicated
values.a) f(-5)
b) f(3)
c) f(0)
d) f(1)
2
3 0
( ) 1 0 2
2 2
x if x
f x x if x
x if x
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Difference Quotient
Ex 4. Evaluate f(x) = 3x – 1 at the following values.
a) f(a)
b) f(a + h)
c) ( ) ( )f a h f a
h
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Class Work
4. Find the difference quotient, for the function:
( ) ( )f a h f a
h
2( ) 2 9f x x
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5. Use the function to evaluate the indicated expression and simplify.
f(x) = 3x – 1 a) f(2x) =
b) 2f(x) =
c) f(x2) =
d) (f(x))2=
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Pg.155 (13-27) odd, 29, 31, 35, 59, 60, 67, 68Pg. 167 (23-26, 55-60) all