IAC U1

Relation

a set ordered pair of real numbers (a graph or equation)

A function

a relation each x- value has one y-value (passes vertical line test)

A one to one

a function where each one x-valye has one y- value (passes vertical and hortizontal line test)

Even function

F(-x)=f(x), has symmetry on the y-axis f(x)=x² F(-x) = (-x)² = x²

Odd function

f(-x)=-f(x), every term must have the opposite charge as it originally did

continuity

a function is continuous if you can draw it without picking up your pen

jump discontinuity

a piece wise function

removable discontinuity

a "hole"

infinite discontinuity

has a vertical asymtope

bounded

the limit of the range

bounded below

bounded above

Relative (Local) maximum

the largest y-value on an interval.

Relative (Local) minimum

the smallest y-value on an interval.

Absolute (Global) extrema

the greatest or smallest y value

y= a * x

vertical stretch a>1

vertical shrink 0<a<1

y = (b *x)

horizontal shrink b>1

horizontal stretch 0<b<1

y = -a *x

y= (-b*x)

reflect over x

reflect over y

y=x²

quadratic

key points = (0,0)(1,1)(-1,1) (2,4) (-2,4)

no asymtopes

bounded below

even

up up

domain= (−∞,+∞)

y=x³

cubic

key points = (0,0)(-1,-1)(1,1) (2,8) (-2,-8)

no asymtopes

unbounded

odd

down up

domain = (−∞,+∞)

y= sqrt x

square root

key points = (1,1) (4,2)

no asymtopes

bounded below

neither odd or even

up

domain = [0,+∞)

y = lnx

natural log

key points = (1,0) (e,1)

x=0 vertical asymtope

neither odd or even

unbounded

down up

domain = (0,+∞)

y=e^x

exponential

key points = (0,1)(1,e)

y=0 horizontal asymtope

neither odd or even

unbounded

down up

domain = (−∞,+∞)

y = 1/x

rational or reciprocal

key points = (1,1)(-1,-1)

y=0 and x=0 vertical and horizontal asymtopes

odd

unbounded

down up

domain = (−∞,0)∪(0,∞)

y = |x|

absolute value

key points = (0,0)(1,1)(-1,1)

no asymtopes

even

bounded below

up up

domain = (−∞,∞)

(fog)(x)

f of g of x

f(g(x))

finding domain

x can not equal

(- infnity, x can not equal)U(x can not equal, infitinty)

x/= 0

(-infinity, 0)U(0,infinity)

fog=x gof=x

fx and gx are the inverse of eachother

finding gx anf fx from fogx

always parent functions

first find gx

then fx

1/1/2

= 2/1

domain and range using imputs and outputs fogx

it will be the domain of g and the range of f

how to find

1. compare range of g to domain of f see if anything matches 2.those that match go to their range

-you have found the range of fogx

3. go back to the range of g

4. find what leads to those numbers

• you have the domian of fogx