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.
252
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