graphs of functions
DESCRIPTION
Graphs of Functions. Lesson 3. Warm Up – Perform the Operations and Simplify. Solution. Solution. Solution. Solution. Domain & Range of a Function. What is the domain of the graph of the function f?. Domain & Range of a Function. What is the range of the graph of the function f?. - PowerPoint PPT PresentationTRANSCRIPT
Warm Up – Perform the Operations and Simplify
2
412.
x
a
5420
3.
22
xx
x
xxb
352
10
5
6112.
2
23
xx
x
x
xxxc
92
7
92
7.
x
x
x
xd
352
10
5
6112.
2
23
xx
x
x
xxxc
Solution
35
106
3125
10612
312
10
5
6112
352
10
5
6112
2
2
23
x
xx
xxx
xxxx
xx
x
x
xxx
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x
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xxx
Let’s look at domain and range of a function using an algebraic approach.
Then, let’s check it with a graphical approach.
Find the domain and range of
Algebraic Approach
.4 xxf
The expression under the radical can not be negative.Therefore, Domain .04 x
,4
4:
or
xA Since the domain is never negative the range is the set of all nonnegative real numbers.
,0
0:
or
yARange
The more you know about the graph of a function, the more you know about the function itself.
Consider the graph on the next slide.
Ex: Find the open intervals on which the function is increasing, decreasing, or constant.
Increases over the entire real line.
Ex: Find the open intervals on which the function is increasing, decreasing, or constant.
,11,
:
and
INCREASING
1,1
:
DECREASING
Ex: Find the open intervals on which the function is increasing, decreasing, or constant.
0,
:
INCREASING
2,0
:CONSTANT
.2
:DECREASING
The point at which a function changes its increasing, decreasing, or constant behavior are helpful in determining the relative maximum or relative minimum values of a function.
Approximating a Relative Minimum
Example: Use a GDC to approximate the relative minimum of the function given by
.243 2 xxxf
Put the function into the “y = “ the press zoom 6 to look at the graph.
Press trace to follow the line to the lowest point.
.243 2 xxxf
Example
Use a GDC to approximate the relative minimum and relative maximum of the function given by
.3 xxxf
Let’s graph a Piecewise-Defined Function
Sketch the graph of
1,4
1,32
xx
xxxf
Notice when open dots and closeddots are used. Why?