AP Precalc Unit 1B Test

what is the horizontal asymptote when the leading terms have the same degree

the leading coefficient

what is the horizontal asymptote when the leading term in the denominator dominates the numeration

y=0

what is the horizontal asymptote when the leading term in the numerator dominates the denominator

NONE

if the numerator has a degree that is exactly one more then the degree of the denominator, then f(x)

has a slant (oblique) asymptote

if the question asks you to find the end behavior as the imput values increase without bound, what does this mean

write your limit for as x—> positive infinity

to find the y-intercept of a rational function…

plug 0 in for x

what does “for what imput values of f are the output values of f equal to 0

what are the zeros

when solving for zeros you have to

watch out for holes but looking at both the numerator and the denominator

REMEMBER VERTICLE ASYMPTOTES (AKA what you are doing to find the domain) ARE NOT

ZEROS

a hole occurs ONLY when the factor in the BLANK fully cancels out with the factor in the BLANK

denominator/ numerator

there will be a verticle asymptote if the

denominator can NOT cancel out with the factors in the numerator

the rate of change is a decreasing rate when the graph is

CONCAVE DOWN

the rate of change is an increasing rate when the graph is

CONCAVE UP

the rate of change is increasing when the graph is

increasing

how to find y coordinate of a hole

plug in the x coordinate of the hole into the function

what is the limit of a hole in either direction?

the y coordinate of the hole

how to find a hole

factor that cancels out in both the numerator and the denominator

what ever is left of your numerator after removing holes is what

your graph with look like

how to find domain

factor denominator

how to find zeros

factor numerator (make sure factors don’t cancel out)

how to find verticle asymptote

factors in denominator that dont cancel out

how to find horizontal asymptote

look at leading degree in numerator and denominator

slant asymptote

when the degree of the numerator is only one more than the degree in the denominator

if you have a positive slant asymptote what is the limit

-∞=-∞ +∞=+∞

how to find equation for slant asymptote

use long division (divide numerator by denominator taking the leading term of the denominator putting it into numerator)

if you are asked for the slant asymptote equation should you include the remainder?

no.

how to find y-intercept

sub in 0 for x

when doing long division, do you need every x degree in the dividend?

YES!! YOU MUST PUT ALL X DEGREES IN IF ITS MISSING. EX: 3x³-2x²+0x-1

translations

rigid movements horizontally or vertically

if the translation is outside of the parentheses is it horizontal or vertical

vertical

if the translation is inside of the parentheses is it horizontal or vertical

horizontal

if a horizontal translation is plus are you moving to the left or right

left

if a horizontal translation is minus are you moving left or right

right

when translating a fuction that has both a verticle reflection and a translation, what should you do first

VERTICLE TRANSLATION!

if you are just giving the domain and range how do you do vertical and horizontal translations

add or subtract horizontal movement from domain

add or subtract vertical movement from range

TRUE OR FALSE: Vertical reflections only affect RANGE

TRUE

when given domain and vertical reflection, what do you do

make all rangle values opposite then add or subtract vertical translation. (MAKE SURE TO WRITE IN CORRECT ORDER AFTER CHANGING TO NEGATIVE IF NEEDED)

What is the order for translations

1. Horizontal

   1. Dilation

   2. Reflection

   3. Translation

2. Vertical

   1. Dilation

   2. Reflection

   3. Translation

Don’t forget the SQUARED in horizontal dilation. if there is a square your horizontal dialation

is the square root of what it would be without the square

inversely proportional equation

y=K/x

What is y in an inversely proportional equation

y is going to be the first things stated before it says inversely proportional

What is x in an inversely proportional equation

the thing stated after it says inversely proportional

What should you remember when solving for values in a piecewise function

UNITS

When looking for horizontal Asympotes make sure that

you look at the highest degree (even if its not in the right order)

describe this translation

down 8 units

describe this translation

right 3 units