3-2 Relations & functions

Front

What is the definition of a function?

Back

A function is a relation where every input has only ONE output.

Front

Is the graph a function if the ordered pairs are (-2, 0), (-1, 1.5), (0, 3), (1, 4.5), (2, 6), (4, 9), (6, 12), (7, 13.5)?

Back

Yes, it IS a function because each input x has exactly one output y.

Front

Is the following relation a function? (1, 2), (1, 3)

Back

No, it IS NOT a function because the input 1 has multiple outputs.

Front

Does this mapping diagram represent a function if input 2 goes to outputs 3 and 4?

Back

No, because an input value goes to multiple output values.

Front

Is the graph a function if it passes the vertical line test?

Back

Yes, if a vertical line intersects the graph at most once, it is a function.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is paired with exactly one input.

Front

What is a mapping diagram?

Back

A visual representation of a function that shows how each input is paired with an output.

Front

If a function is defined as f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.