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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