Download - Pre-Calculus Review
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: