Integrated Algebra 1

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Integrated Algebra 1

• 1.9 Absolute Value Functions

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Vocabulary

• The absolute value of a number c is the distance
  between c and zero on a number line. (ALWAYS
  POSITIVE)
• c represents the value of c
• Absolute value functions are transformations of
  the parent function f(x) x.

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Graph of parent function for absolute value
functions.

• f(x) x

-2
-1
0
1
2
2
1
0
1
2
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Horizontal Shift

• g(x)xh this is a horizontal shift to the
  right.

g(x)xh this is a horizontal shift to the left.
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Vertical Shift

• g(x)xk this is a vertical shift up.

g(x)x-k this is a vertical shift down.
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Vertical Stretch

• g(x)ax is a vertical stretch by a factor of a.

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Vertical Shrink

• g(x) x is a vertical shrink by a factor of
  .

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Vertical Stretch and Shrink

• g(x)-ax and g(x) - x cause the graph
  to open down.

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Describe the transformation

• g(x)x5

This is a horizontal shift 5 to the right.
This is a horizontal shift 5 to the left.
g(x)x5
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Describe the transformation

• g(x)x7

This is a vertical shift 7 units up.
This is a vertical shift 7 units down.
g(x)x-7
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Describe the transformation

• g(x)-5x

A vertical stretch by 5 units and opens down.
This is a vertical shrink and opens up.
g(x).6x
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Graph of parent function for absolute value
functions.

• f(x) x-3

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Graph the function

• f(x) -x5

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Graph the function

• f(x) 2x

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Homework

• p.53 1-15 all