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Precalculus
Unit 1 Cheat Sheet
Parent Functions
Transformations
Key Features of Functions
Function Value Domain/Range Increasing/Decreasing Y-intercept/Zeros/Roots
Given
Solve for
Take the value
inside
parameters (the
parenthesis) and
plug in every
time you see your
variable
Domain: values of X that the
function can have
Range: values of Y that the
function can have
Increasing (Directly
Proportional):
Decreasing (Indirectly
Proportional):
y-intercept: Where the function hits the
y-axis. It should be in the form ( 0 , ๐ฆ)
zero: Where the funciton hits the x-axis.
It should be in the form (๐ฅ, 0 )
Symmetry and Even/Odd
Property Testing Symmetry
Use the following test. If you return the EXACT same
equation, it has symmetry โwith respect toโ the test
x-axis Replace ๐ฆ โ โ๐ฆ
y-axis Replace ๐ฅ โ โ๐ฅ
origin
Replace ๐ฆ โ โ๐ฆ
Replace ๐ฅ โ โ๐ฅ
Precalculus
Unit 1 Cheat Sheet
Even/Odd/Neither
Change the sign of ALL โxโ.
Follow the test to see what your function is.
Even Return original: ๐
Odd
Return ALL signs changed: ๐(โ๐) = โ๐(๐)
Neither Return something funky
Compositions
Property Blob Method
Given
2
Solve for
[
]
First Term
BLOB
2
Second Term
PARENTHESIS
Now, follow the first term. Copy everything down exactly as you see it, UNTIL you
get to a blob. When you see a blob, copy down a parenthesis AND everything inside
the parenthesis
[
](
2
Real World Compositions
Procedures Creating Equations from Word Problems
- Create at least 2 equations from the word problem
- Using your equations, perform compositions (both ways)
- Plug in and solve! (remember, to check if you are solving for x or y)
http://goo.gl/2SEGco
Inverses
What is an inverse? Solving inverses
An inverse can pass the horizontal line test.
An inverse is symmetric to the original function with respect to the line ๐ฆ = ๐ฅ.
Algebraic:
- Change your function name to โyโ
- Switch you โyโ and โxโ
- Solve for new โyโ
Graphical
- Make a table and put function coordinate points in
- Switch you โxโ and โyโ in the coordinate points
- Plot points and connect dots
- Is it symmetric with respect to ๐ฆ = ๐ฅ?
Continuity, Limits, End Behavior
Continuity Limits End Behavior
Continuity โ can I draw the function without
picking up my pencil?
My limit EQUALS my function at that point
lim
๐ฅโ๐
๐(๐ฅ) = ๐(๐)
- Test the limit from the left
- Test the limit from the right
- Does the limit exist?
- Test the function value
- Does the limit equal the function?
Limits โ APPROACH!
Limits are NOT functions
The limit from the left must equal the limit from the
right for the limit to exist
lim
๐ฅโ๐
โ
๐(๐ฅ) = lim
๐ฅโ๐
๐(๐ฅ)
End Behavior โ What is the graph doing at the ends
of the graph!
Use limit notation
