Pre-Calculus ReviewPart 1

Transformations

Compositions

Graphs Domain Even/Odd The Inequality of it All!

The inverse

100 100 100 100 100 100 100

200 200 200 200 200 200 200

300 300 300 300 300 300 300

400 400 400 400 400 400 400

500 500 500 500 500 500 500

Given f(x) = sin(2x -1)

a. Find the zeros of f(x).

b. Sketch the graph of f(x). Be sure to label any intercepts.

Graphing

Graphing

Given f(x) =

Sketch the graph of f(x). Be sure to label any asymptotes and intercepts.

2ln 4x

Graphing

F(x) =

Sketch the graph of F(x). Be sure to label any asymptotes and any intercepts.

3

3

4 16

8

x x

x

Graphing

( ) 5 1f x x x

Sketch the graph of f(x). Be sure to label any asymptotes

and any intercepts.

Graphing

Sketch the graph of f(x). Be sure to label any asymptotes and any intercepts.

2ln( 5)( ) xf x e

Composition

29 xIf f(x) = and g(x) = 2

1

xfind f(g(x)).

Composition

29 xIf f(x) = and g(x) = 2

1

xSketch the graph of g(f(x)).

Composition

If f(x) = x2 – 4x + 3 and g(x) = ln(x), find g(f(x)).

Composition

If f(x) = x2 – 4x + 3 and g(x) = ln(x), sketch the graph of g(f(x)).

Composition

Let f(x) be an even function and g(x) be an odd function, show that f(g(x)) is an even function.

Domain?

State the domain of .2( ) ln 4f x x

Domain?

State the domain of .2

1( )

9f x

x

Domain?

State the domain of .3 2( ) ln( 2 5 6)f x x x x

Domain?

State the domain of .2( ) 3 2f x x x

Domain?

State the domain of .1

( )2 3

f xx

Even/Odd/Neither?

Is the following function even, odd, or neither? Justify your answer analytically.

3

2( )

x xf x

x

Even/Odd/Neither?

Is the following function even, odd, or neither? Justify your answer analytically.

2ln( 5)( ) xf x e

Even/Odd/Neither?Is the following function even, odd, or neither? Justify your answer analytically.

( ) sin(2 )f x x

Even/Odd/Neither?Is the following function even, odd, or neither? Justify your answer analytically.

24 16( )

4

x xf x

x

Even/Odd/Neither?Is the following function even, odd, or neither? Justify your answer analytically.

tan( )

sin

xf x

x

TransformationsGiven the graph of f(x), sketch the graph of f(|x|).

(2,9)

(-2,-8)

-1

1

f(x)

TransformationsGiven the graph of f(x), sketch the graph of |f(x)|.

(2,9)

(-2,-8)

-1

1

f(x)

TransformationsGiven the graph of f(x), sketch the graph of lnf(x).

(2,9)

(-2,-8)

-1

1

f(x)

Transformations

Given the graph of f(x),

sketch the graph of .

(2,9)

(-2,-8)

-1

1

f(x)

( )f x

TransformationsGiven the graph of f(x), sketch the graph of f(2x - 1)+1.

(2,9)

(-2,-8)

-1

1

f(x)

Solve for x.

2 3 10x

Solve for x.

2

2 30

1 1

x

x x

Solve for x.

2 22 3 4 0x x x

Solve for x.

3 1 2 1 1x x

Solve for x.

4 12

1

x

x x

Inverses

3( )

4f x

x

Write an equation for the inverse of the function

Inverses

Write an equation for the inverse of the function

f(x)= x2 – 4x – 5, if x > 2

Inverses

sin(cos -1 (-0.5))Evaluate

Inverses

cot (tan -1 (3/4))Evaluate:

Inverses

sec -1 (x) = cos -1 (1/x)Prove: