Domain, Range, Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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

How do you find f(0) for the function f(x) = -3(x-1)?

Back

To find f(0), substitute 0 for x: f(0) = -3(0-1) = 3.

Front

Is y a function of x if each x-value corresponds to multiple y-values?

Back

No, if each x-value corresponds to multiple y-values, then y is not a function of x.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

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 is the notation for domain?

Back

The domain is often denoted as D(f) or simply as the set of x-values for which the function is defined.

Front

What is the notation for range?

Back

The range is often denoted as R(f) or simply as the set of y-values that the function can take.

Front

If the domain of a function is x ≥ 2, what does this mean?

Back

This means that the function is defined for all x-values that are greater than or equal to 2.