Year 2 Chapter 2: Functions And Graphs Flashcards
What is |-x| equivalent to?
X
What is |X| equivalent to?
X
When f(x) < 0, what is |f(x)| equivalent to?
-f(x)
When f(x) > 0, what is |f(x)| equivalent to?
f(x)
When you have a graph of y= |ax + b|, how do you sketch it?
. Sketch y=ax+b but then reflect the section of the graph below the x-axis in the x-axis (the reflected section is also known as ‘y= -1(ax+b)’.
. This means none of your graph is below the x-axis.
What is a modulus function?
Where y=|f(x)|
Name 2 types of functions and a third type that isn’t actually a function (explain what these 3 are):
. One-to-one: For every output there is one input.
. Many-to-one: For every output there are more than one inputs
. One-to-many (not a function): For one input, there are more than 1 outputs.
Define domain:
The set of all possible inputs for a mapping.
Define range:
The set of all possible outputs for a mapping
Define composite functions (give example):
. When two or more functions can be combined to make a new function.
. fg(x)
What is gh(x) equivalent to?
g(h(x))
Inverse of f(x) and give an expression that it is not the same as (but is easy to think that it’s the same as):
Equivalent to f^(-1)(x) but different to (f(x))^-1.
What does the inverse of a function do?
. Takes the elements in the range of the original function and maps them back into elements of the domain of the original function.
. Domain of f(x) is the range of f^-1(x).
. Range of f(x) is the domain of f^-1(x).
What line do you reflect y=f(x) into to get y=f^-1(x)?
y=x
How do you find the inverse of a given function?
. Do y= given function.
. Rearrange so you get x = …..
. Change the y letters in ‘…..’ to x letters.
. Then the ‘…..’ is inverse function.
