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Parabola f(x)= a(x-h) 2
(-3-h)^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 |
(x-3)2 -5 --> |
move to the right |
If parenthesis is addition, move to the left |
Graph the functions. Plot at least 3..
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Make a table for eqaution |
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pick points for x |
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Solve |
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graph answers |
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should be in the form of f(x)=bx |
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) = ax2+bx+c is a parabola |
f(x)= x2+k |
f(x)= (x-h)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 |
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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 bx =x |
log (xy) = log (x) + log (y) |
blog 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 |
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
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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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