LAST MATHEMATICIAN STANDINGReview 1.4-1.6

PROBLEM 1

Find f(g(x)) and f(f(x)).( ) , ( )f x x g x x 22 3 4

PROBLEM 1 - ANSWERS Find f(g(x)) and f(f(x)).

( ) , ( )

( ) ( )

( ( )) ( )

f x x g x x

f g x x

xf f x x

x

2

2

2

2 3 42 4 32 52 2 3 34 9

PROBLEM 2

Find f(g(x)) and its domain.

( ) , ( )f x g x xx

1 22

PROBLEM 2 Find f(g(x)) and its domain.

Domain of f(g(x)) is ( 2 , ∞ )

( ) , ( )

( ( ))

f x g x xx

f g xx

1 2212 2

PROBLEM 3

f(x) = g(x) =

( ( ))f g xx

2

15

PROBLEM 3

f(x) = g(x) =

( ( ))f g xx

2

15

1x

2 5x

PROBLEM 4

g(x) = f(x) =

( ( )) ( )g f x x 24 5

PROBLEM 4

g(x) = f(x) =

( ( )) ( )g f x x 24 5

4x 2 5x

PROBLEM 5

Find the inverse of h(x).

( )h xx

1

4

PROBLEM 5

Find the inverse of h(x).

( )h xx

1

4

( )h xx

1 1 4

PROBLEM 6

Find g(f(-1)).

( ) , ( )f x x g x x 26 2 4

PROBLEM 6

Find g(f(-1)).

( ) , ( )f x x g x x 26 2 4( ) ( )( )

( ) ( )( )( ( ))

ff

ggg f

2

1 6 2 11 8

8 4 88 256

1 8

For the remaining problems, give the basic function and all the vertical and horizontal transformations in the correct order! Be sure to mention where the horizontal and vertical asymptotes are.

PROBLEM 7

( ) ( )f x x 23 6

PROBLEM 7 Basic Function is

Horizontal SHIFT right 6

Horizontal shrink BAFO 1/3rd

( ) ( )f x x 23 62( )f x x

PROBLEM 8

( )f x x 4 3

PROBLEM 8

Basic Function is Horizontal SHIFT right 4

Vertical SHIFT up 3

( )f x x 4 3

( )f x x

PROBLEM 9

( )f x e 22 7

PROBLEM 9

Basic Function is Vertical STRECTH BAFO 2Vertical SHIFT up 7 HA is at y = 7

( ) xf x e

( )f x e 22 7

PROBLEM 10

( ) ln( )f x x 4 6

PROBLEM 10

Basic Function is Reflection over the x-axisVertical SHIFT up 6 Horizontal SHRINK BAFO 1/4th

VA is at X=0

( ) lnf x x

( ) ln( )f x x 4 6

PROBLEM 11

( ) ( )f x x 32 1

PROBLEM 11

Basic Function is Reflection over the y-axisHorizontal SHRINK BAFO 1/2

Vertical SHIFT up 1

3( )f x x

( ) ( )f x x 32 1

PROBLEM 12

( ) sin( )f x x 3 5

PROBLEM 12

Basic Function isHorizontal SHIFT left 5 Horizontal SHRINK BAFO 1/3rd

Reflection over the y-axis

( ) sinf x x

( ) sin( )f x x 3 5

PROBLEM 13

( )f x x 12 43

PROBLEM 13

Basic Function isHorizontal STRETCH BAFO 3 Vertical STRETCH BAFO 2Reflection over the x-axisVertical SHIFT down 4

( )f x x

( )f x x 12 43

PROBLEM 14

( )f x x 31 72

PROBLEM 14

Basic Function isReflection over the y-axis Vertical SHRINK BAFO 1/2

Vertical SHIFT down 7

3( )f x x

( )f x x 31 72

PROBLEM 15

( )f x x 1 4 22

PROBLEM 15

Basic Function isHorizontal SHIFT right 4Horizontal STRETCH BAFO 2

Vertical SHIFT up 2

( )f x x

( )f x x 1 4 22

PROBLEM 16

Find and its domain.

( )f x x 2 6( )f x 1

PROBLEM 16

Find and its domain.

Domain of inverse is [ 0, ∞ )

( )f x x 2 6( )f x 1

( )f x x 1 2 6