3-2 Families of Graphs

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3-2 Families of Graphs

• Pre Calc A

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Parent Graphs
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Parent Graphs
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Changes to Graph
Dilations Vertical y c f(x) cgt1
stretch 0ltclt1 Compression Horizontal y
f(cx) cgt1 compression 0ltclt1 stretch
Reflections Over x-axis y -f(x) Over y-axis y
f(-x)
Translations Up y f(x) c Down y f(x)
c Left y f(x c) Right y f(x c)
Other Changes y f(x) reflects any part of
the parent graph that is below the x-axis, so
that it is above the x -axis
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Ex 17

• Use the parent graph y x³ to sketch the graph
  of each function

y (x 1)³
y x³ - 1
y (x 1)³ 3
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Ex

• Graph the function and describe the movement

f(x) (x 1)² - 2
f(x) (x 1)² - 2