Algebra - Functions

absolute value is...

distance from zero on the number line

absolute value is ALWAYS...

positive

distance can NOT be...

negative

compound statements are...

made up of more than one equation

compound statements come in two forms...

disjunctions & conjunctions

interval of increase

x coordinates

interval of decrease

y coordinates

horizontal shift

f(x) → f(x-h)

h < 0 moves ...

moves right

h > moves...

moves left

vertical shift

f(x) → f(x) + k

k > 0 moves ...

moves up

k < 0 moves ...

moves down

reflection across y-axis

f(x)→ f(-x)

reflection across y-axis value

input value

reflection across x-axis

f(x) → -f(x)

reflection across x-axis value

output value

horizontal stretch/compression

f(x) → f (⅟b X)

b > 1 moves...

stretches away from the y-axis

0 < |b| < 1 moves...

compresses toward the x-axis

vertical stretch/compression

f(x) → a ⋅ f(x)

line becomes steeper...

stretched vertically or compressed horizontally

line becomes flatter...

compressed vertically or stretched horizontally

multiple transformations given?

create a temporary function to represent each function before moving on to the next function

function notation

Flashcard: Function notation is a way to represent a function using symbols. It typically involves using f(x) to represent the output of a function when given an input x.

function domain

Function Domain:The set of all possible input values (x-values) for which a function is defined. It determines the valid inputs that can be plugged into a function to produce an output.

function range

The range of a function is the set of all possible output values it can produce.