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Tim N.

An even Equation

when a graph is symmetric to the y-axis. If you plug in -x for x the equation does not change

Average Rate of change

= slope. change in y - change in x/ y-x

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vertex of an equation

(-b/2a,(f)-b/2/a)

discriminent

b-scuared-4ac

Function

For each input there is only one out put.

Find domain of a square root

set < to 0. the (-infin,4) =x<4

f+g

(f+g)x=(f)x+(g)x

x can split up with each variable

see if point is in an equation

plug in the integer that coordinates with the given variable in the equation

Odd equation

symmetrical to the origin cubed unless negative than neither

Neither equation

when it is neither symmetrical to the y axis or origin

average rate of change for a squared function

Y2-Y1/X2-X1

`Secant line

the average rate of change is the slope in a secant line containing two points on that line. plug in the two points to find the rate of change. than plug in xy values and slope to Y=mx+b

Absolute value graph

even unless shifted to the right or left

Square root graph

half of a parabola. unless shifted the graph is in 1 quadrant

Square function

even unless shifted to right or left

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Cube function

odd unless shifted to the right or left

graph Shifted on vertical plane

goes up if k is positive and down if k is negative

graph shifted on horizontal plane

when positive graph shifts to the left and when negative to the right

Vertical stretch

when the coefficient before the variable is larger than 1

Vertical compression

when the coefficient before the variable is less than 1

reflection across the x axis

f(x)= -f(x)

reflection across the y axis

f(x)=f(-x)

quadratic equation

f(x)=ax squared +bx+c = f(x)=a(x+h)squared+K

equation to find H

-b/2a

equation for k

4ac-bsquared/4a

find vertex with out graphing

find what h is by plugging into -b/2a and than plug h back into the equation h=x

maximizing an enclosed area

area=length*width

divide both the width and height by two to get the variables by themselves

determining degree

0 has a degree of 0

what does a non polynomial graph look like

has either cusp, corner gap or hole

power function

f(x)=ax raised to the N degree

zeros

zeros are the x intercepts

behavior near a zero

even degree will touch and an odd degree will cross the x axis

turning point

a graph can have as many turning points as one less than the degree

end behavior

even positive-both point up

even negative-both point down

odd possitive- one up to the right one down to the left

odd negative- one up to the left one down to the right

steps for anayzing the graph of a polynomial

find the x intercepts by plugging in 0 for y

find the y intercept by plugging in 0 for x

determine if the graph crosses or touches at each intercept

find the degree and figure out the end behaviors

determine the maximum number of turning points by looking at the deree

to find minima or maxima

find -b/2a and than plug back in to equation

Rational function

r(x)=p(x)/q(x)

Reciprocal Function

f(x)=1/x

Vertical Asymptotes

whatever the zeros are in the domain

Horizontal asymptotes

if numerator degree is smaller than the denominator than the asymptote is 0

If the degree is the same in both numerator and denominator than you divide the coefficients

If the numerator degree is larger than the denominator than there is an oblique asymptote

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