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Higher Mathematics > 3. Functions > Flashcards

3. Functions Flashcards

1
Q

What is a function like

A

A number machne

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2
Q

Input of function

A

Domain (x)

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3
Q

Domain (x)

A

An input of function

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4
Q

Output of function

A

Range (y)

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5
Q

Range (y)

A

Output of function

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6
Q

How are functions written

A

f (x)

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7
Q

Given g (x) = 3x^2 - x, find the value of g (x-2)

A

3x2 - 13x + 14

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8
Q

Method for solving basic function

A
  1. Write our function
  2. Sub domain into function
  3. Simplify
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9
Q

If h(x) = x / (2x +3), simplify h (1/x)

A

1 / 2 + 3x

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10
Q

Two restrictions on domain

A

You can’t take the square root of a -ve

You can’t divide by 0

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11
Q

What does a restriction on the domain mean

A

Function will be undefined for a certain value of x

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12
Q

Find for

A
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13
Q

Find for what value (s) of x is f(x) undefined and state a suitable domain

for (x) = /(x-3)

A

x is undefined when x - 3 < 0, x < 3

domain = x greater than or equal to 3

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14
Q

Find for what value (s) of x is f(x) undefined and state a suitable domain

f(x) = 1 / x(x+5)

A

x ≠ 0, -5

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15
Q

Set

A

Collection of items with a common property

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16
Q

Collection of items with a common property

A

Set

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17
Q

Element/member

A

An item in a set

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18
Q

An item in a set

A

Element/member

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19
Q

N set

A

Natural numbers

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20
Q

Natural numbers

A

N

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21
Q

W set

A

Whole numbers

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22
Q

Whole numbers

A

W set

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23
Q

Z set

A

Integers

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24
Q

Integers

A

Z set

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25
Q

Q set

A

Rational numbers

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26
Q

Rational numbers

A

Q set

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27
Q

R set

A

Real numbers

28
Q

Real numbers

A

R set

29
Q

Order of sets

A

N
W
Z
Q
R

30
Q

Order of sets

A

N
W
Z
Q
R

31
Q

E =

A

Belongs to

32
Q

Empty set

A

No elements in a set

33
Q

No elements in a set

A

Empty set

34
Q

3 ways functions can be written

A

Equations, arrow diagrams, graphs

35
Q

What must you ensure when writing a function as a arrow diagram

A

Each domain only links to one member of the range

36
Q

Displaying function as graph

A

Domain is x coordinate

Range is y coordinate

37
Q

Composite function

A

Function that combines more than one function

38
Q

Function that combines more than one function

A

Composite function

39
Q

Method for solving composite functions

A
  1. Find internal function by subbing x into bracketed equation
  2. Solve equation
  3. Sub answer into outer function
  4. Solve equation
40
Q

If f(x) = 3x + 7 and g(x) = 5x, find f (g(x)) when x is 7

A

112

41
Q

Given f(x) = 2x + 3, what is h(x) if h (x) = f (x / (x+1))

A

5x + 3 / x + 1

42
Q

Inverse function

A

Each element in B links to one element in A

43
Q

Each element in B links to one element in A

A

Inverse function

44
Q

Of the original function multiplies by 5, what is the inverse

A

Divided by 5

45
Q

Method of finding inverse function from original function

A
  1. Change f(x) to y
  2. Change subject of formula to x
  3. Swap x for f-1 and swap y for x
46
Q

Find the inverse of f(x) = 4x + 3

A

f-1 (x) = x - 3 / 4

47
Q

Find the inverse of f(x) = 4x + 3

A

f-1 (x) = x - 3 / 4

48
Q

Order of operations in finding inverse functions

A

Opposite of bodmas

49
Q

Find the inverse of f(x) = 1/3 (x+7)

A

f-1(x) = 3x - 7

50
Q

Find f(f-1(x)) if f(x) = 5x + 2

A

x

51
Q

applying a function to its inverse or vice versus gives…

A

x

52
Q

How can the graph of an inverse function be found

A

By reflecting the graph of f(x) in the line y=x

53
Q

By reflecting the graph of f(x) in the line y=x

A

Find graph of inverse

54
Q

Coords of inverse in relation to function

A

The x and y coordinates switch

55
Q

Exponential function form

A

f(x) = a^x

or

y = a^x

56
Q

f(x) = a^x

or

y = a^x

A

Exponential

57
Q

Anything to the power of 0 =

A

1

58
Q

What points does an exponential pass through

A

(0, 1) and (1, a)

59
Q

what graph passes through (0, 1) and (1, a)

A

Exponential

60
Q

Direction of exponential graph if a > 1

A

Up from left to right

61
Q

Direction of exponential graph if 0 < a < 1

A

Down from left to right

62
Q

Form of log function

A

y = logax

63
Q

y = logax

A

Logarithmic graph

64
Q

Log graphs are the inverse of what

A

Exponential functions

65
Q

Inverse of exponential functions

A

Logarithmic functions

66
Q

What points do a log graph pass through

A

(1, 0) and (a, 1)

67
Q

What always passes through (1, 0) and (a, 1)

A

Logarithmic graph

Higher Mathematics (7 decks)

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