Functions and Graphs Flashcards

1
Q

In terms of sets, what does ‘N’ mean? Give examples.

A

Natural numbers

1,2,3,4,5,6,7,8,etc

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2
Q

In terms of sets, what does ‘W’ mean? Give examples.

A

Whole numbers

0,1,2,3,4,5, etc

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3
Q

In terms of sets, what does ‘Z’ mean? Give examples.

A

Integers
-2, -1, 0, 1, 2
Any number, including zero, and positive and negative numbers, as long as the number isn’t an decimal/fraction

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4
Q

In terms of sets, what does ‘Q’ mean? Give examples.

A

Rational numbers

-4, 1/3, 0.25, 3

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5
Q

In terms of sets, what does ‘R’ mean? Give examples.

A

Real numbers
Every number
-4, 3, 4.2, 7/8

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6
Q

How do you write a set?

A

{xEN : 1 < x < 5}
where E = is a member of
where N = natural numbers

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7
Q

What are you asked to do in SET questions and how do you do it?

A

List all possible numbers (x) can be
P = {xEN : 1 < x < 5}
then P = 2, 3, 4

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8
Q

What are the rules when dealing with functions?

A
  • Can’t divide by zero

- Can’t find the square root of a negative

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9
Q

What is a domain?

A

A set of inputs

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10
Q

What is a range?

A

A set of possible outputs

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11
Q

How are function questions asked and how do you answer them?

A

A function g is defined by (equation). Define a suitable domain for g.

Domain = {xER : x!=4}
or {xER : x > 2}
etc

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12
Q

How do you complete composite functions?

A

Write out both equations
g(f(x)) = g(whatever f(x) is)
Sub f(x) into the x’s of g(x)
Simplify

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13
Q

How do you find inverse functions?

A
Write out equation
Change function (f(x)) to y
Make x the subject
Put equation into f-1(x)
Change the y to an x
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14
Q

For graph transformations, what does f(x) + a, mean?

A

Move the graph up by a

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15
Q

For graph transformations, what does f(x) - a, mean?

A

Move the graph down by a

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16
Q

For graph transformations, what does f(x + a), mean?

A

Move the graph left by a

17
Q

For graph transformations, what does f(x - a), mean?

A

Move graph right by a

18
Q

For graph transformations, what does -f(x), mean?

A

Flip on x-axis

mirror on x-axis

19
Q

For graph transformations, what does f(-x), mean?

A

Flip on y-axis

20
Q

For graph transformations, what does af(x), mean?

A

Change vertical scale
if a=2, double scale
if a=1/2 = half scale

21
Q

For graph transformations, what does f(ax), mean?

A

Change horizontal scale
if a = 2, half scale
if a = 1/2, double scale