Graph transformations: Vertex Form
Changing a function using transformations
A local sports center, with a swimming pool, gym, tennis courts, and more,
sells a yearly memberships at a price that depends on member age.
Children under the age of 10 are admitted free; then, the
price increases every 5 years. Prices are designed so that
both teenagers and senior citizens pay less than adults.
The following function describes the dependence of the cost
of a yearly membership on member age.
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After some time, it is decided to change the price schedule
to satisfy one of the following demands:
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Membership will be free for youth under 16.
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.1
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Membership will be free for people below the age of 20 and above the age of 80.
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.2
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Membership will be free for people below the age of 20 and above the age of 100.
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.3
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Membership will be free for people below the age of 6 and above the age of 54.
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.5
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Membership will be free for people below the age of 15.
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.4
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The maximum fee will be payed by subscribers of age 40.
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.5
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The maximum cost of a membership will be $100.
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.6
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The maximum price of $200 will be paid by members whose
age is 45.
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.7
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All memberships will cost 20% less than the current
price.
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.8
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All memberships will cost $20 less than the current
price.
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.9
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Making tranformations
on the graph is convenient way of performing these changes.
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Perform the changes suggested above through
transformations of the graph.
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Perform the following transformations on the given function f(x) and check
whether the resulting function can represent the suggested change
(you can use the
Translations and Stretching tools):
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Horizontal translation.
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Vertical translation.
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Combination of horizontal and vertical translation.
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Horizontal stretching.
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Vertical stretching.
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Combination of horizontal and vertical stretching.
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| Record the changes you think are
effective and practical, and the correspondence rules that
result. If, in your opinion, the change is not appropriate, explain
why.
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