Lesson 2 Shift and Stretch Solidify Understanding
Jump Start
Graph each function:
1.
2.
3.
Learning Focus
Transform the graph of
Write equations from graphs.
Predict the horizontal and vertical asymptotes of a function from the equation.
What other functions can be made from
Open Up the Math: Launch, Explore, Discuss
In the previous lesson, you were introduced to the function
1.
Use the graph of
Horizontal Asymptote:
Vertical Asymptote:
Anchor Points:
Now you’re ready to use this information to figure out how the graph of
In each of the following problems, you are given either a graph or a description of a function that is a transformation of
2.
Equation:
3.
Equation:
4.
The function has a vertical asymptote at
Equation:
5.
Equation:
6.
The function has a vertical asymptote at
Equation:
7.
Equation:
8.
Equation:
9.
The function has a vertical asymptote at
Equation:
10.
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___
___
___
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Reflection over the
-axis. Vertical shift of
, making the horizontal asymptote . Horizontal shift left
, making the vertical asymptote . Vertical stretch by a factor of
. Horizontal shift right
, making the vertical asymptote .
11.
Graph each of the following equations without using technology.
a.
b.
12.
Describe the features of the function
Vertical asymptote:
Horizontal asymptote:
Vertical stretch factor:
Domain:
Range:
Ready for More?
You have already named the asymptotes and other features of
Takeaways
Transformations of
Try one more:
Lesson Summary
In this lesson, we learned to graph functions that are transformations of
1.
Find the domain of
2.
Find all of the roots of
Roots:
Factored form: