functions

studied byStudied by 46 people
5.0(1)
get a hint
hint

function

1 / 36

Tags and Description

37 Terms

1

function

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

  • passes “vertical line test”

New cards
2

domain

  • all possible x-values

  • input, dependent variable

  • use interval notation

New cards
3

range

  • all possible y-values

  • output, dependent variable

  • use interval notation

New cards
4

continuity

  • no breaks in the graph

  • a “continuous” curve

New cards
5

removable discontinuity

  • the graph can be repaired by filling in a single point

  • hole(s) in the graph

New cards
6

jump discontinuity

  • a break in the graph

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

New cards
7

infinite discontinuity

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

  • there is a vertical asymptote

New cards
8

increasing interval

  • as x goes up, y goes up

  • positive slope

  • use x-values for the interval

New cards
9

decreasing interval

  • as x goes up, y goes down

  • negative slope

  • use x-values for the interval

New cards
10

constant interval

  • as x goes up, y stays the same

  • 0 slope

  • use x-values for the interval

New cards
11

relative/local maximum

  • point where the graph changes from inc. to dec.

  • could be more than one

New cards
12

relative/local minimum

  • point where the graph changes from dec. to inc.

  • could be more than one

New cards
13

absolute maximum

  • highest point on the graph

  • only one

  • if positive or negative infinity, none

New cards
14

absolute minimum

  • lowest point on the graph

  • only one

  • if pos. or neg. infinity, none

New cards
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

New cards
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

New cards
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 -∞

New cards
18

bounded below

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

    • have an absolute minimum

New cards
19

bounded above

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

    • have an absolute maximum

New cards
20

bounded

when the graph is bounded above and below

New cards
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

New cards
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

New cards
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

New cards
24

indentity/linear

f(x)=x

<p></p>
New cards
25

quadratic

f(x)=x^2

knowt flashcard image
New cards
26

cubic

f(x)=x^3

knowt flashcard image
New cards
27

reciprocal

f(x)=1/x

knowt flashcard image
New cards
28

square root

f(x)=\|x

knowt flashcard image
New cards
29

exponential

f(x)=e^x

knowt flashcard image
New cards
30

logarithmic

f(x)=lnx

knowt flashcard image
New cards
31

absolute value

f(x)=|x|

knowt flashcard image
New cards
32

sine

f(x)=sinx

knowt flashcard image
New cards
33

cosine

f(x)=cosx

knowt flashcard image
New cards
34

greatest integer

f(x)=[x]

knowt flashcard image
New cards
35

logistic

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

knowt flashcard image
New cards
36

1/x^2

knowt flashcard image
New cards
37

3\|x

knowt flashcard image
New cards

Explore top notes

note Note
studied byStudied by 13 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 12 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 17 people
Updated ... ago
5.0 Stars(2)
note Note
studied byStudied by 7 people
Updated ... ago
4.0 Stars(1)
note Note
studied byStudied by 24 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 2 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 7 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 184 people
Updated ... ago
5.0 Stars(2)

Explore top flashcards

flashcards Flashcard86 terms
studied byStudied by 27 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard122 terms
studied byStudied by 25 people
Updated ... ago
5.0 Stars(2)
flashcards Flashcard20 terms
studied byStudied by 34 people
Updated ... ago
5.0 Stars(4)
flashcards Flashcard78 terms
studied byStudied by 3 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard22 terms
studied byStudied by 74 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard45 terms
studied byStudied by 8 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard49 terms
studied byStudied by 25 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard90 terms
studied byStudied by 8024 people
Updated ... ago
4.4 Stars(62)