Functions and Graphs

Question 1

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

Answer 1

Natural numbers

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

Question 2

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

Answer 2

Whole numbers

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

Question 3

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

Answer 3

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

Question 4

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

Answer 4

Rational numbers

-4, 1/3, 0.25, 3

Question 5

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

Answer 5

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

Question 6

How do you write a set?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

What are the rules when dealing with functions?

Answer 8

• Can’t divide by zero

- Can’t find the square root of a negative

Question 9

What is a domain?

Answer 9

A set of inputs

Question 10

What is a range?

Answer 10

A set of possible outputs

Question 11

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

Answer 11

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

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

Question 12

How do you complete composite functions?

Answer 12

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

Question 13

How do you find inverse functions?

Answer 13

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

Question 14

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

Answer 14

Move the graph up by a

Question 15

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

Answer 15

Move the graph down by a

Question 16

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

Answer 16

Move the graph left by a

Question 17

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

Answer 17

Move graph right by a

Question 18

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

Answer 18

Flip on x-axis

mirror on x-axis

Question 19

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

Answer 19

Flip on y-axis

Question 20

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

Answer 20

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

Question 21

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

Answer 21

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