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Unit 3: Transforming Graphs of Functions3.1: Translating Graphs of Functions

1) Vertical Translations

If a function y=f(x) becomes y=f(x)+k we say that the function hasbeen translated (moved) UP k units.Therefore; y=f(x) ­ k has been translated DOWN k units.

We saw this in Grade 11 when we moved the vertex of the parabola.

Sketch y=x2 and then sketch y=x2+3

Sketch and then sketch

Notice we were shifting simple radical graphs in the last unit.

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2) Horizontal Translations:

When y=f(x) is translated to y=f(x­h) the function is translated (moved) h units right.Therefore y=f(x+h) is moved h units to the left.Again we can translate functions we are familiar with:Draw a sketch of:1) y = (x ­ 2)22) 3)y=(x­2)3

If we put both of these translations together, we end up with

y=f(x­h)+k

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Example Questions:

1)

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2)

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Writing an equation from the given translation statement:

3)

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4)

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5)

a) The graph would be translated ____units _______(direction).

b) The graph would be translated ____units _______ and also ____units ________.

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Homework: Pg 169#4­14, 16 Mult Choice 1,2