Topic 2 functions and graphs

Question 1

What is a modulus function

Answer 1

A function of the type y=lf(x)l

Question 2

How do you sketch a modulus function

Answer 2

Sketch the function within the modulus normally, then reflect the line in the x axis where the line meets the x axis

Question 3

What is a domain

Answer 3

What numbers are allowed to be inputs to the function

Question 4

What is the range (range and domain)

Answer 4

What numbers are possible outputs from the function

Question 5

What is a mapping

Answer 5

A function if every input has a distinct output.

Question 6

With mapping, what are the 2 types of functions

Answer 6

• One to one
• Many to one

Question 7

What does a mapping transform

Answer 7

One set of numbers into a different set of numbers

Question 8

Explain why the function must be one-to-one for an inverse function to exist

Answer 8

If the mapping was many-to-one, then the inverse mapping would be one-to-many, which is not a function

Question 9

When finding out the inverse function, what is the easiest method
e.g. find the inverse of y=2x+1

Answer 9

• Rearrange the equation to make x the subject
  2x=y-1
  x=(y-1)/2
• Then swap x and y
  y=(x-1)/2
  and that’s the inverse function

Question 10

When sketching the function and it’s inverse functions, how is this done

Answer 10

Reflect the original function in y=x, this will graph the inverse. So just swap the x,y coordinates so it’s now y,x