Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
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Exercise 13 Page 20

Determine which operation should be used for each transformation and apply the desired transformations in order.

g(x)=1/3x+2/3

Practice makes perfect

To write the function rule g(x), let's look at possible transformations. Then we can more clearly decide which operations should be used to apply the desired transformations to the parent function.

Horizontal Translations
Translation right h units, h>0 y=f(x- h) Translation left h units, h>0 y=f(x+ h)
Using the table, let's apply the given transformation, a translation 4 units to the left, by substituting (x+ 4) for each x-term.
f(x)=1/3x-2/3
f( x+4)=1/3( x+4)-2/3
f(x+4)=1/3x+4/3-2/3
f(x+4)=1/3x+2/3
Next, we can replace f(x+4) with g(x) and complete the function rule. g(x)=1/3x+2/3