Domain, Range, and Functions

Front

What is the domain of a function?

Back

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

Front

How do you determine the domain of a function from its graph?

Back

Identify the x-values for which the graph exists; these values make up the domain.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a function is defined for all real numbers?

Back

The domain of the function includes every possible real number.

Front

What is an example of a function with a restricted domain?

Back

f(x) = √x, where the domain is x ≥ 0.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3.

Front

What is the range of the function f(x) = x^2?

Back

The range is y ≥ 0, since the output of x^2 is always non-negative.

Front

How can you express the domain using set notation?

Back

For example, {x | -2 ≤ x ≤ 4} represents all x values from -2 to 4, inclusive.

Front

What is a function?

Back

A relation where each input (x) has exactly one output (y).