Math Unit 1B

If there is a hole it can not be a

zero

If it doesn’t cancel out in the denominator

its not a hole, its a vertical asymptote

For end behavior if the limit is getting really small and close to zero the end behavior is

lim f(x)=0

If it is a hole that # can not be a

vertical asymptote

If their is a horizontal asymptote then the end behavior is

lim f(x)= the horizantal asymptote

Degrees are the same horizantal asymptote=

Leading coefficient

To find where f(x) is less or greater than 0

use domain and zero values to make a table

For vertical asymptote you have to say

to the left/right

Degree on top is bigger horizantal asymptote=

none

Degree on bottom is bigger horizontal asymptote=

0

If you have to do all translations the order is

Left or right, reflection, up or down

f(x+4)

(opposite) Left 4

-f(x)

reflection

Limit notation for a hole

lim g(x)= y intercept of hole

x->x intercept of hole

f(x) + y (y=4)

go up whatever y is…so y = 4

Form for pascals triangle if it were 4th power

1a⁴b⁰+ 4a³b^{1 …}

To find the zeros look at the

numerator

for vertical asympotote the f(x) only equals BLANK as x approaches BLANK

infinity/ neg infinity, vertical asymptote

To find vertial asymptote look at

denominator

To find the domain of the rational function look at

the denominator

When determining the end behavior of a rational function without a hole,vertical/horizantal asymptote, or slant slant asymptote look at the

leading coeficient to see if its pos/neg infinity

When looking to see if it increases or decreases look at the line from

left to right

If you have to make a table for f(x) is less than something etc use

domain and zero values to make the table

inverse problems

y=k/x k=constant of proportionality

use brackets when

value is included in interval

(x/2)

multiply by 2!!!

Inside: m(-x)

Reflect over the y-axis

Outside: -m(x)

Reflect over the x-axis

if it asks to desribe the transformation for x transformation u say BLANK

horizontally

if it asks to desribe the transformation for y transformation u say BLANK

vertically

the denominator has to fully cancel out for there to be a

hole