Functions

Question 1

How to a show a function is even

Answer 1

Show that f(x) = f(-x)

Question 2

How to show a function is odd

Answer 2

Show that f(x) = -f(-x)

Question 3

Domain

Answer 3

The range x values that can go into a function

Question 4

Range

Answer 4

The range of y values that can be outputted from a function

Question 5

Calculating complex ranges and domains

Answer 5

Cannot divide by 0 and cannot sqrt -n, use combination of these to develop domain/ range.
Often be a mix (triganometric? e.e. tan(x))

Question 6

Domain restriction

Answer 6

In order to invert functions they must be strictly increasing. What we can do is restrict the values we input into our function such that our function is invertible. E.g. restricting tan(x) between -pi/2<x<pi/2

Question 7

What will an even function look like?

Answer 7

Reflected about the y axis

Question 8

What will an odd function look like?

Answer 8

Reflected about the x and y axis

Question 9

What makes a function a function?

Answer 9

It is one to one(e.g. one distinct y value for every x value, e.g. a circle is not a function

Question 10

Finding inverse functions

Answer 10

We can find these by switching the variables and then resetting.

Question 11

Properties of inverse function

Answer 11

Inverse( original (x))=x

Question 12

Interval notation

Answer 12

Infinities will be surrounded by (), if there is a value that is included it will be in a [] bracket, if there is a value excluded within the domain then join with union and have )U(