Transformations of Functions

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Transformationsof Functions

• Viviana C. Castellón
• East Los Angeles College
• MEnTe
• Mathematics Enrichment
• through Technology

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Graph
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• Given the following function,
• If a gt 0, then shift the graph a units up
• Ifalt 0, then shift the graph a units down

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• Given the following function,
• Since a gt 0, then the graph will be
• shift up 5 units

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Lets graph
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• Given the following function,
• How will the graph look?

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Lets graph
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• Given the following function,
• Since a lt 0, then the graph will be
• shift down 3 units

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Lets graph
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• Given the following function,
• How will the graph look?

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Lets graph
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Given the following function,

• For this equation, b is inside the parenthesis.
• We get the expression and equal it to zero.
• If b gt 0, then shift the graph b
• units right
• If b lt 0, then shift the graph b
• units left

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• Given the following function,
• We get the expression and equal it to zero.
• Since b lt 0, then shift the graph
• 2 units left

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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• Recall
• a gt 0 then shift up
• a lt 0 then shift down
• Equal the expression to zero
• b gt 0 then shift to the right
• b lt 0 then shift to the left

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Given the following function,
For this equation, c determines how wide or thin
the parabola will be. if cgt1, then the graph
is closer to the y-axis if c1, then the graph
remains the same if 0ltclt1, then the graph is
further from the y-axis if c is a negative
number, then the graph will reflect on the x-axis
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Lets graph
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Given the following function,
Since cgt1, then the graph is closer to the
y-axis
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Lets graph
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Lets graph

• How will the graph look?

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Lets graph
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Lets graph

• How will the graph look?

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Lets graph
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• Recall
• agt0 then shift up
• alt0 then shift down
• Equal the expression to zero
• bgt0 then shift to the right
• blt0 then shift to the left
• if cgt1, then closer to the y axis
• if c1, then the graph is the
• same
• if 0ltclt1, then further from
• the y axis

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Lets graph

• How will the
• graph look?

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Lets graph

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Congratulations!!You just completed the
transformation of