Studied by 46 people

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hint

1

function

a rule that assigns every x-value to exactly one y-value

passes “vertical line test”

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2

domain

all possible x-values

input, dependent variable

use interval notation

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3

range

all possible y-values

output, dependent variable

use interval notation

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4

continuity

no breaks in the graph

a “continuous” curve

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5

removable discontinuity

the graph can be repaired by filling in a single point

hole(s) in the graph

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6

jump discontinuity

a break in the graph

if you trace the graph, you would have to jump to the next point

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7

infinite discontinuity

two or more pieces of the graph approach positive or negative infinity

there is a vertical asymptote

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8

increasing interval

as x goes up, y goes up

positive slope

use x-values for the interval

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9

decreasing interval

as x goes up, y goes down

negative slope

use x-values for the interval

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10

constant interval

as x goes up, y stays the same

0 slope

use x-values for the interval

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11

relative/local maximum

point where the graph changes from inc. to dec.

could be more than one

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12

relative/local minimum

point where the graph changes from dec. to inc.

could be more than one

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13

absolute maximum

highest point on the graph

only one

if positive or negative infinity, none

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14

absolute minimum

lowest point on the graph

only one

if pos. or neg. infinity, none

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15

vertical asymptote

x=a is a va if f(x)→∞ or if f(x)→∞

to find, set the denominator of a function’s equation equal to zero

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16

horizontal asymptote

y=b is a ha if f(x)→b as x→∞ or as x→-∞

graphically, see where the ends of the graph go

algebraically, if the degree of the denominator is greater than the degree of the numerator, ha: y=0

if the degree of the denominator is less than the degree of the numerator, ha: none

if the degrees are equal, y=quotient of leading coefficients

the degree of a function is the highest exponent

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17

end behavior

the behavior at the left and right ends of the graph

as x→-∞, what does y approach?

as x→∞, what does y approach?

right eb: approaches ∞

left eb: approaches -∞

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18

bounded below

there is some number b that is less than or equal to every number in the range

have an absolute minimum

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19

bounded above

there is some number b that is greater than or equal to every number in the range

have an absolute maximum

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20

bounded

when the graph is bounded above and below

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21

even functions

y-axis symmetry

for each point (x,y) on the graph, the point (-x,y) is on the graph

f(-x)=f(x)

all graphs with y-axis symmetry are even functions

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22

not functions

for each point (x,y) on the graph, the point (x,-y) is on the graph

all graphs with x-axis symmetry are not functions

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23

odd functions

for each point (x,y) on the graph, the point (-x,-y) is on the graph

f(x)=-f(x)

all graphs with y-axis symmetry are odd functions

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24

indentity/linear

f(x)=x

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25

quadratic

f(x)=x^2

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26

cubic

f(x)=x^3

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27

reciprocal

f(x)=1/x

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28

square root

f(x)=\|x

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29

exponential

f(x)=e^x

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30

logarithmic

f(x)=lnx

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31

absolute value

f(x)=|x|

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32

sine

f(x)=sinx

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33

cosine

f(x)=cosx

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34

greatest integer

f(x)=[x]

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35

logistic

f(x)=1/1+e^-x

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36

1/x^2

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37

3\|x

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