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methods > functions and relations > Flashcards

functions and relations Flashcards

1
Q

domain

A

horizontal distance

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2
Q

range

A

vertical distance

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3
Q

if there is no stated domain or range?

A

assume it is R

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4
Q

how to find domain and range of a coordinate set

A

list the x values for domain and the y values for range

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5
Q

function

A

a relation where no coordinates has the same x value

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6
Q

vertical lines test

A

determines if it is a function

must interest once

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7
Q

what is a restriction?

A

a function but with a smaller domain

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8
Q

one to one functions

A

every x value has a different y value

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9
Q

horizontal line test

A

one intersection and it is one-to-one

two intersections and it is many to one

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10
Q

how do you sketch a piecewise function?

A

sub in the value of the domain to find the y point and then sketch the graph normally keeping in the domain

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11
Q

odd function

A

-f(x) = f(-x)

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12
Q

even function

A

f(-x) + f(x)

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13
Q

formula for the addition of ordinates

A

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

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14
Q

rule for composite functions

A

fog(x) = f(g(x))

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15
Q

domain of composite functions

A

the domain of the inner function

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16
Q

rules for inverse functions

A

must be one-to-one to have an inverse

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17
Q

domain and range of inverse functions

A

domain of inverse is the range of the function and the range of the inverse is the domain of the function

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18
Q

how to find the inverse?

A

swap x and y and solve for y

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19
Q

power functions

A

x^r where r is a rational number

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20
Q

strictly increasing and strictly decreasing

A

the turning point is included

21
Q

odd positive integer for power functions

A

goes through the first and third quadrants with a stationary point at 0,0
- gets steeper as the number increases

22
Q

even positive integer for power functions

A

quadratic shape

- gets steeper as the number gets bigger

23
Q

odd negative integer

A

hyperbola shape

24
Q

even negative integer

A

trunks shape

25
Q

even fractional power

A

half quadratic in first quadrant

26
Q

odd fractional power

A

half quadratic in first quadrant and double reflection of that in the third quadrant
- an s

27
Q

how do you solve linear literal equations?

A

normally

28
Q

how do you solve simultaneous linear literal equations

A

normally

29
Q

what is the distance formula?

A

square root of (x2-x1) squared + (y2-y1) squared

30
Q

what is the midpoint formula?

A

x1+x2 divided by 2 and y1+y2 divided by 2

31
Q

gradient of a straight line

A

rise over run

32
Q

tangent of an angle of a slope

A

m= tan(angle) where the angle is the angle made with the positive x axis

33
Q

perpendicular line

A

m1 x m2 = -1

34
Q

parallel line

A

m1 = m2

35
Q

how do you calculate the shape of areas

A

divide into shapes you can calculate the areas of

36
Q

entries

A

numbers in a matrix

37
Q

dimension of a matrix

A

the number of rows and columns

38
Q

rows or columns listed first

A

rows and then columns

39
Q

when does A =B in matrices?

A
  • same number of rows and columns

- same entries at the same points

40
Q

how do you add matrices?

A

add the corresponding numbers

41
Q

how do you subtract matrices?

A

subtract the corresponding numbers

42
Q

A + A (matrices)

A

= 2A

43
Q

how do you multiply matrices?

A
  • multiply the first entry of row 1 of A by the first entry of column 1 of B
  • add that to the second entry of row 1 of A by the second entry of column 1 in B
  • only works if dimensions are the same
44
Q

does AB = BA?

A

no

45
Q

unique solution?

A

one intersection

46
Q

no solutions?

A

parallel

47
Q

infinite solutions

A

same line

48
Q

how to solve linear equations with more than two variables

A

eliminate a variable and then solve normally

- do this by multiplying or subtract etc.

methods (3 decks)

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