Section 1.3; Page 99

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Section 1.3 Page 99
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Domain and Range
has no meaning when x is 0 ?
Domain is input range is output
has no meaning when x is negative ?
Set of numbers for which the function is defined
is called the domain of the function.
Only valid for x between -2 and 2 inclusive
Range, the values of y (function) can take
x -20.12 y sqrt(4 - x.2) plot (x,y)
This is similar to example 6
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Numerator x 0
We need to satisfy the conditions for the
numerator and the denominator ? 0 x lt 2
Denominator should be both positive and greater
than 0
For tow products to be positive, they both must
be positive
Numerator -2 x 2
function 0 lt x 2
Denominator x gt 0
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Section 1.5
Shifting, Reflecting, and Stretching Graphs
Summary of Graphs of Common Functions
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Vertical and Horizontal Shifts (p126)
Note shift to the right
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- ? DOWN
- ? RIGHT
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? SHIFT LEFT
1 ? SHIFT UP
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SHIFT LEFT ?
SHIFT DOWN ? -
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Reflecting Graphs
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SUBSTITUTE -x for x
MULTIPLY THE WHOLE BY -
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Page 128
Flip and add move right by 3 ? -3
Flip and add 2
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Nonrigid Transformations
a change in the shape of the original graph
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1.6 Combinations of Functions
Just simply write it separately
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Try this please
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Ignore this and look at the same example we did
last class on slide 5
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Compositions of Functions
Pay attention to new symbol
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Now to be fancy, refer to n as a function h(x),
and m as a function f(x)