Chapter 2 Functions and graphs - Year 2

Question 1

What does this graph look like?
What happens if you start to transform it? (Simple translations)

Answer 1

As you move the graph around the y axis will mirror what is on the x axis
Also the x axis will mirror what is on the y axis
(So you will always know the y intercept and where it cuts or touches the x axis)

Question 2

How do you draw a mod graph?

Answer 2

Method 1) Draw the normal graph (without the mods) then reflect whatever is below the x axis into the positive x plane

Question 3

How do you solve modulus problems?

Answer 3

You need to draw them out to see where the interceptions are
Then you need to:(if the answer is in the non reflected bit delete the mods and solve normally)
(If the answer is in the reflected bit then negative whatever is in the modulus, then solve normally)

Question 4

What is the domain of a function?

Answer 4

The posible inputs into a function

(Vertical lines)

Question 5

What is the range of a function?

Answer 5

The set of all posible solutions to a function

Question 6

What is a function?

Answer 6

A function is a special type of mapping such that each member of the domain is mapped to 1 and only 1 element in the range

Question 7

What do I always forget to do when writing the range of a function?

Answer 7

I forget tp say f(x) and not x

Question 8

What are the different types of mappings?

Answer 8

Many to 1
1 to many
1 to 1

Question 9

What type of mapping is a function?

Answer 9

1 to 1

Question 10

What type of mapping is a quadratic?

Answer 10

Many to 1

Question 11

What is a piecewise functon?

Answer 11

A function which is defined in parts so we can use different rules for different intervals of the range

Question 12

What do you do with a piecewise function at the point in which 1 graph stops and the other begins?

Answer 12

You literally stop (draw a little circle to represent the fact that that point isn’t included in the graph and then start drawing the next graph.

If the domain has an (less or grater) than AND equal to then you colour in the circle to show that

Question 13

How do you work out a composite function in terms x?

Answer 13

You substitute the latter function into the primary function (wherever there is an x)

Question 14

What must be true about a function for it to have an inverse function?

Why?

Answer 14

It must be 1 to 1 for an inverse function to exist

Because if the mapping was many to 1 then the inverse mapping would be 1 to many but this is nit a function

Question 15

What is the method to find the inverse of a function

Answer 15

Put it equal to y then re arranged to make x the subject

Question 16

What do you need to remember to do when working out the inverse function?

Answer 16

Write the inverse function out in terms of x

Question 17

How do you find the inverse function of y=a quadratic?

Answer 17

You complete the square on the quadratic

Question 18

What are 3 useful facts about inverse functions?

Answer 18

They do the opposite of the original function
They are a mirror of the original function in the line y=x so any solutions to the equation will be on the line y=x
The domain of the function = the range of the inverse function
The range of the function = the domain of the inverse function

Question 19

When doing questions in all topics what do you need to be mindful about your answers?

Answer 19

If the question states the domain only that part of the graph matters. If there are solutions which are outside the domain/range then they don’t matter

(Could calculations need to stay within the domain)

Question 20

How do you draw a graph of

Answer 20

Draw the normal graph and then anything below the x axis is reflected above it

Question 21

How do you draw a graph of

Answer 21

You reflect it in the y axis

Question 22

What is a common mistake when solving modulus questions?

Answer 22

People negative everything but you are only supposed to negative the mod bit

Question 23

In which order do you do the transformations?