CATA Unit 3 Concepts

College Algebra Trig A

what is the rule for input and outputs of functions?

can have multiple x’s but not multiple y’s (vertical line test)

x rule for functions

cannot have multiple y outputs

y rule for functions

can have multiple x’s

even function equation

f(-x)=f(x)

odd function equation

f(-x)=-f(x), you can factor out a -1 and within the () should be the original f(x)

what do odd roots mean for the domain?

(-∞, ∞) always

what do even roots mean for the domain?

set the expression to be ≥ 0

how do you put turning points in interval notation?

if both lines include it, they are excluded () in notation

reflecting over x axis impacts

the y outputs

vertical stretch impacts

y points

-A means

points reflect over x axis, multiply by it

| A | > 1 means

stretch, multiply by it

-B means

reflect over the y

|B| > 1 means

you compress by multiplying by the reciprocal

0 < |B| < 1 means

you stretch by multiplying by the reciprocal

-C means

you add to the x, move to the right

+C

you subtract to the x, move to the left

+D means

add to y, move up

-D means

subtract to y, move down

constant, certain quadratics, absolute values are all

even

linear, cubic, cube root, and reciprocals are all

odd

exponential and square roots are

neither

when there is a quadratic on the bottom how do you find the domain?

set it ≠ 0 and factor to domain

equation for average rate of change

f(x2)-f(x1) / x2 - x1

A and D

impact the y

B and C

impact the x

cubic equations look like

square root equations look like

reciprocal equations

y= a/x

f(x) + 3

up 3

f(x +3)

left 3

f(4x-3)

multiply x by ¼ then add 3

-2f(x)+1

reflect over x by multiplying, up 1 by adding

how do you algebraically check if a function is one to one?

set the equation equal to itself and make one side x sub 1 and the other x sub 2

what is the difference quiotient?

f(x+h) - f(x) / h

how do you find the domain of a square root function?

set it more than or equal to zero

how do you find the domain and range of the inverse of a function?

the domain of the OG function is the range of inverse, and range of the OG function is the domain of the inverse

how do you test if an equation is one to one?

horizontal line test, no repeating xs or ys

how do you find the domain of a polynomial over another?

factor the denominator and those are the excluded points

how can do you make something one to one?

create domain restriction so it passes the horizontal line test

can you square root > or < equations?

never, have to factor and test critical points