Functions & Function Notation

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is function notation?

Back

Function notation is a way to denote functions using symbols, typically written as f(x), where f is the function name and x is the input.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

What does it mean for a set of values to be a function?

Back

A set of values is a function if no two ordered pairs have the same first element (input) but different second elements (output).

Front

Evaluate the function f(x) = 2x + 3 for f(4).

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Is the mapping {(1,2), (2,3), (1,4)} a function?

Back

No, it is not a function because the input 1 is associated with two different outputs (2 and 4).

Front

If g(3) = 12, what point does this represent?

Back

The point (3, 12) is represented by g(3) = 12.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 3x + 2.