Unit 6 · Functions & Function Notation
A function assigns each input exactly one output. Graphs, tables, mapping diagrams, and equations can all represent functions.
Two different inputs may share an output (y = x²). One input may not have two outputs. That is the vertical line test.
A relation in which each input has exactly one output.
Example: The rule “output is 3 more than input” is a function.
The set of all possible inputs.
Example: For f(x) = √x, the domain is x ≥ 0.
The set of all possible outputs.
Example: For f(x) = x², the range is y ≥ 0.
Try the prompt first. The steps stay folded until you ask to see them.
Does the table (1,4), (2,4), (3,9) represent a function? What about (1,4), (1,5)?
Watch for
Thinking repeated outputs mean it is not a function
Repeats are a problem only on the input side.
Fix: Scan the x-values, not the y-values.
Submit each answer to check it. The key is not shown until you do.
Which function has a domain of all real numbers and a range greater than or equal to three?
A table of values represents a function. Which statement describes the function?
Which set of ordered pairs represents a function?
Use mapping diagrams with arrows: two arrows from one input is the red flag.
Restrict a circle x² + y² = 25 to a function by taking the upper semicircle.
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