pre calc final

domain

x values

range

y values

rise

change in y

run

change in x

includes end point

⬤,[ ], ≤,≥

does not include end point

○,( ), <,>

zeros

where the graph touches or crosses the x axis

positive interval

points that lies above x axis

negative interval

points thay are below x axis

when is there a possibility for a open circle in a piecewise function

on the boundary line

Odd multiplicity

crosses the x axis

even multiplicity

touches x axis

the degree

the highest exponent

the leading coefficient

the number in front of the highest exponent

if the leading cof is positive the end behavior…

goes up

if the leading cof is negative the end behavior…

goes down

what does a even degree function mean

it means that the LEB and REB will go the same way

what does a odd degree function mean

it means that the LEB and REB will go opposite directions

if the leading coefficient is pos the REB goes up

So the LEB will go down

if the leading cofficient is negative the REB will go down

so the LEB will go up

left =

-∞

right =

∞

to find the y intercept of a function…

set x= to 0

to find zeros

factor the function and set each part to 0

exponential

f(x)=B^x

natural base

e

e=

2.718281828

anything to the power of 0 is

1

inverse of exponential=

log function

if y=B^x then

log_b Y

how to solve exponent

1. isolate what's raised to exponenet

2. Log with matching base to both sides to cancel exponent

3. do operations if needed to isolate variable

Multiplication exponential

x^m X xⁿ = x^m+n

Divison exponential

x^m /xⁿ = x^m-n

power exponential

(x^m )ⁿ = x^mn

multiplication log

log_b (X x Y )= Log_b x +log_{b Y}

divison log

log_b (x/y)= log_b x - log_b Y

power log

log_b (x^r )= R x Log_b x

Ln cancels

e

transformation function

f(x)= a* F(x-h)+K

+H

moves left

-H

right shift

+K

shift up

-K

shift down

-f(x)

reflection

A*F(x) (a>0)

vertical stretch

A*F(x) (0<A<1)

vertical shrink

identity function

y= x

squaring function

y=x²

cubing function

y=x³

square root function

y=√x

cube root function

y=³√x

absolute value function

y=|x|

you only need to find a domain restriction for rational if only only 1 problem

domain restriction occurs when denominator=0

synthetic divison

1. Find the box number by setting the second poly = to 0

2. 2. If one exponent is missing dont’t skip add a 0

IVT

1. Determine if function is continuous

2. Plug both endpoints into the function

3. Determine if 0 lies between both of the answers

When solving a log or exponential question with a negative number

You must flip it to make it positive

if there is no number with log the number is

10