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Parabola f(x)= a(xh) 2
(3h)^2 
h determines x axis 
( 2 negatives= positive) 
If a is positive parabola is up or to the right 
Vertex is at (h,k) 
if a is negative opens left or down 
(x3)^{2} 5 > 
move to the right 
If parenthesis is addition, move to the left 
Graph the functions. Plot at least 3..

Make a table for eqaution 

pick points for x 

Solve 

graph answers 

should be in the form of f(x)=b^{x} 
Graph the functions. plot at least.. (Rules)
if b>1 its a exponential growth function 
if 0<b<1 its a exponential decay function 
if b>1 Domain = ( infinity, infinity) 
if b>1 Range = (0,infinity) 
if b>1The line y=0 is horizontal asympote 
if b>1 Function passes through (0,1) 
Quadratic functions of the form
Shifting Parabolas
f(x) = ax^{2}+bx+c is a parabola 
f(x)= x^{2}+k 
f(x)= (xh)^{2} 
a>0 opens up 
is a vertical shift of f(x)=x^2 
h>0 shifted right vice versa 
a<0 opens down 
k>0 shifted up vice versa 


x (possible extra terms here)= square root of b
Steps: get it in the form of the equation by adding and subtracting different sides
Apply sqaure root and the plus or mins sign
Find the inverse
Change f(x) to y 
Switch x & y 
Solve for y 
Don't forget about cross multiplying
Logarithms
log 1=1 
Only solve multiple logs if they have the same base 
log b^{x} =x 
log (xy) = log (x) + log (y) 
b^{log sub bx} =x 
log 1=0 
log b=1 
power is what it's equal to
base is the sub
Solve log equation.
Convert to exponential form based off of note 
Simplify 
2^{3}= 8 which is log 8 = 3
Solve using Substitution.
Substitute the same terms with a letter 
Solve for the letter ex: (x=2) 
Replace the letter with what was in the equation 
Solve 
Solve the inequality using the test point method


Solving a Polynomial Inequality EX
Solving a Polynomial Inequality
Think of it as a Quadratic equation (< OR > as a = sign) 
Solve equation 
Plot answers 
Pick numbers from each A,B,C 
if equation is tue part of solution 
if false not part of solution 
find and write out solution set 
Solve the equation b = c
Get bases same by putting a power or square root or fraction 
Cross out bases 
Exponents become base 
Solve equation 
Sometimes doesnt look like example, general it has 2 numbers raised to a power with an equal sign between
Graphing inverse
Look at > or < sign, determines what part of parabolas are the answer 
Find the inverse 
plot parabola from solved equation "y=..." 
Make a table of points 
f and g functions
replace f and g perform operation in middle 
Horizontal line test 
(g ∘ f )(x) = g(f(x)) 
intersects more than once, not a function 

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