# functions

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## Tags and Description

### 37 Terms

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

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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