2.2 ) Functions

Question 1

What are the different number sets ?

Answer 1

• Natural numbers ( N )
• Whole numbers ( W )
• Integers ( Z )
• Rational numbers ( Q )
• Irrational numbers ( R / Q )
• Real numbers ( R )

Question 2

What are Natural numbers ( N ) ?

Answer 2

All positive integers not including zero

Question 3

What are whole numbers ( W ) ?

Answer 3

All positive integers including zero

Question 4

What are Integers ( Z ) ?

Answer 4

All positive and negative integers, including zero

Question 5

What are rational numbers ( Q )?

Answer 5

• All positive/ negative integers including zero
• Recurring/ terminating decimals and fractions

Question 6

What are irrational numbers ( Q / R ) ?

Answer 6

Surds, pi, e …

Question 7

What are real numbers ( R ) ?

Answer 7

All numbers apart from complex / imaginary numbers

Question 8

What are the different types of functions ?

Answer 8

• One-one function
• Man-one function

Question 9

What is a one-one function ?

Answer 9

If every y value corresponds to only one x value

Question 10

What is a many-one function ?

Answer 10

At least one y value comes from more than one x value

Question 11

What are the different tests used on a graph to tell whether it is a function ?

Answer 11

• Horizontal line test
• Vertical line test

Question 12

What does a vertical line test show ?

Answer 12

If a mapping is a function, any vertical li e will meet the graph at most once

Question 13

What does a horizontal line test show ?

Answer 13

If a function is one-one, any horizontal line will meet the graph at most once

Question 14

What is the domain of a function ?

Answer 14

The set of allowed x values

Question 15

What is the range of a function ?

Answer 15

The set of possible y/ output values

Question 16

How else can the composite function f(fx) be written ?

Answer 16

• f o f(x)
• f^2 (x)

Question 17

How do you find the inverse of a function ?

Answer 17

• Make the function an equation containing y and x
• Rearrange for x
• Substitute y as x, and x as f^-1(x)

Question 18

Geometrically, how would you describe the f^-1(x) graph relative to f(x) ?

Answer 18

The graph y = f^-1(x) is a reflection of y = f(x) in the line y = x

Question 19

What is the relationship of the domain/ range between f^-1(x) and f(x) ?

Answer 19

• The domain of f(x) is the range of f^-1(x)
• The range of f(x) is the domain of f^-1(x)

Question 20

When do functions have an inverse ?

Answer 20

Only one-one functions have inverses

Question 21

How can you prove a function does not have an inverse ?

Answer 21

• Differentiate and show that the graph has a turning point ( increases and decreases )
• Complete the square to show multiple x values can produce the same output