2.2.2.2.6666 –––– Transformations of FunctionsTransformations of FunctionsTransformations of FunctionsTransformations of Functions Math 141Math 141Math 141Math 141 Warnock - Class Notes

1. How will the graphs of ( ) 2 2g x x= + and ( ) 2 3h x x= − compare to

( ) 2f x x= ?

x ( )f x ( )g x ( )h x

5

-5 5

-5

2. How will the graphs of ( ) ( )23g x x= − and ( ) ( )22h x x= + compare to

( ) 2f x x= ?

x ( )f x ( )g x ( )h x

5

-5 5

-5

3. How will the graph of ( ) 3g x x= − compare to ( ) 3f x x= ?

x ( )f x ( )g x

4. How will the graph of ( )g x x= − compare to ( )f x x= ?

x ( )f x ( )g x

5

-5 5

-5

5

-5 5

-5

5. How will the graphs of ( ) 22g x x= and ( ) 21

2h x x= compare to ( ) 2f x x= ?

x ( )f x ( )g x ( )h x

5

-5 5

-5

6. Sketch the graph of ( ) ( )22 3 4f x x= − −

5

-5 5

-5

7. Given the graph of ( )f x sketch the graph of ( ) ( )3g x f x= and ( ) 1

3h x f x

= ?

5

-5 5

-5

8. Given the function ( ) 4 23 2 4h t t t= + − evaluate ( )h t− .

9. Given the function ( ) 34 7g t t t= − evaluate ( )g t− .

10. Determine whether the following functions are even, odd, or neither.

a) ( ) 5 1g x x= −

b) ( ) 6h t t t= +

c) ( ) 5 3p s s s= +