Functions and Graphs Flashcards
In terms of sets, what does ‘N’ mean? Give examples.
Natural numbers
1,2,3,4,5,6,7,8,etc
In terms of sets, what does ‘W’ mean? Give examples.
Whole numbers
0,1,2,3,4,5, etc
In terms of sets, what does ‘Z’ mean? Give examples.
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
In terms of sets, what does ‘Q’ mean? Give examples.
Rational numbers
-4, 1/3, 0.25, 3
In terms of sets, what does ‘R’ mean? Give examples.
Real numbers
Every number
-4, 3, 4.2, 7/8
How do you write a set?
{xEN : 1 < x < 5}
where E = is a member of
where N = natural numbers
What are you asked to do in SET questions and how do you do it?
List all possible numbers (x) can be
P = {xEN : 1 < x < 5}
then P = 2, 3, 4
What are the rules when dealing with functions?
- Can’t divide by zero
- Can’t find the square root of a negative
What is a domain?
A set of inputs
What is a range?
A set of possible outputs
How are function questions asked and how do you answer them?
A function g is defined by (equation). Define a suitable domain for g.
Domain = {xER : x!=4}
or {xER : x > 2}
etc
How do you complete composite functions?
Write out both equations
g(f(x)) = g(whatever f(x) is)
Sub f(x) into the x’s of g(x)
Simplify
How do you find inverse functions?
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
For graph transformations, what does f(x) + a, mean?
Move the graph up by a
For graph transformations, what does f(x) - a, mean?
Move the graph down by a