Question

functions
what are functions?
__________________________are rules that state every input has exactly one output. functions can be found with charts/graphs, tables, words, equations, or mappings.
looking at the coordinate plane, inputs are the ________ and outputs are the __________. the inputs are referred to as the __________, and the outputs are referred to as the__________________.
coordinate plane image with domain (x - axis) and range (y - axis) labeled
a common example of a function is the __________________________.
how many birthday’s do you have? each person has exactly ______________ birthday. therefore, a birthday is a function.
function notation
function notation box: y = f(x) with labels output, rule, input
this is read ______________.
the rule affects how the input creates the output.
piecewise functions – in the function, there are different ____________ for different __________________.

Explanation:

1. For the first blank: "Functions" are rules where each input has one output.
2. On the coordinate plane: Inputs (x - values) are the horizontal axis (Domain), outputs (y - values) are the vertical axis (Range). Inputs are Domain, outputs are Range.
3. Birthday example: Each person has exactly one birthday (so "one").
4. Function notation \( y = f(x) \) is read "y equals f of x".
5. Piecewise functions: Different rules for different intervals of the domain.

Answer:

1. Functions
2. x - values (or Domain - related, but x - values are inputs); y - values (or Range - related, y - values are outputs); Domain; Range
3. one
4. y equals f of x
5. rules; intervals of the domain (or input intervals)

(Note: For the fill - in - the - blanks related to the coordinate plane, the more precise answers based on function terminology are: inputs are the \( x \) - values (or Domain), outputs are the \( y \) - values (or Range); inputs are referred to as the Domain, outputs as the Range.)