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2.1 Rad Functions and Transformations.notebook
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radical function a function that involves a variable in the radicand.
Chapter
Chapter 2
2.1 Radical Functions and TransformationsPages 62 77
Examples:
2.1 Rad Functions and Transformations.notebook
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Investigating radical functions:1. Complete the following table for . Sketch the resulting table on the axis provided. State the domain and the range.
x y
0
1
4
9
D: R:
2.1 Rad Functions and Transformations.notebook
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2. Complete example 1 b) and c) on page 63 using what you know about transformations and the standard table from #1.
b) D:
R:
c) D:
R:
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3. Complete example 2 on page 65 using what you know about transformations and the standard table from #1.
a) D:
R:
b) D:
R:
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Example 1: Your TurnPage 64
Sketch the graph of the function y = √x + 5 using mapping notation and tables of values. State the domain and the range.
Answer
2.1 Rad Functions and Transformations.notebook
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Example 2: Your TurnPage 68
a) Sketch the graph of the function y = –2√x + 3 –1 by transforming the graph of y = √x .b) Identify the domain and range of y = √x and describe how they are affected by the transformations.
Answer
2.1 Rad Functions and Transformations.notebook
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Example 3: Your TurnPage 69
a) Determine two forms of the equation for the function shown. The function is a transformation of the function .b) What is the equation of the curve reflected in each quadrant?
Answer
2.1 Rad Functions and Transformations.notebook
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Describe in words how to transform the base radical graph to:
a)
b)
c)
More Examples:
1.
2.1 Rad Functions and Transformations.notebook
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2. Write the equation of the radical function that results by applying each set of transformations to the graph of:
a) A horizontal stretch by a factor of 4, then 6 units right.
b) A reflection over the x axis, then 4 units lefts, and 11 units down.
c) A reflection over the y axis, a horizontal stretch by a factor of 1/5, and a vertical stretch by a factor of 3.
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3. Describe how the graph of can be obtained from the graph of .
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