Algebra 2 Companion Book, Volume 2

9.1.3 Transforming Functions − Worksheet

Example 1: Given f x ( ) =

x

x

  

0

3 if

, write the rule for each function.

x

x

4

if

0

>

1. g ( x ), a horizontal translation of f ( x ) 6 units left

2. h ( x ), a horizontal compression by a factor of 1 4

Example 2: Identify the x - and y -intercepts of f ( x ). Without graphing g ( x ), identify its x - and y -intercepts. 3. f x x g x f x () 4 12and () ( ) = + = 4. f ( x ) = − x 2 + 16 and g ( x ) = f (4 x )

1 6

Example 3: Given f ( x ) , graph g ( x ). 5. f ( x ) = − x 2 + 1 and g ( x ) = f (2 x ) − 1

6. f ( x ) = | x − 1| − 2 and g ( x ) = − 2 f ( x )

Example 4: 7.  The state income tax in Connecticut is modeled by the function T x ( )

  

x 0.02 if 0

x < ≤ >

10,000

,

=

x x

0.05 if

10,000

where x is income in dollars. Suppose that Connecticut decided to increase its tax rates by 20% and add a filing fee of $100 dollars. Write a function for the new state income tax.

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