Domain and Range of 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 vertical line test?

Back

The vertical line test is 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 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 the domain from a set of ordered pairs?

Back

To find the domain from a set of ordered pairs, list all the unique x-values from the pairs.

Front

How do you find the range from a set of ordered pairs?

Back

To find the range from a set of ordered pairs, list all the unique y-values from the pairs.

Front

Is the graph of a circle a function?

Back

No, the graph of a circle is not a function because a vertical line can intersect it at two points.

Front

What does it mean if a function has repeating x-values?

Back

If a function has repeating x-values, it means that for at least one input, there are multiple outputs, which violates the definition of a function.

Front

Given the function f(x) = x^2, what is the domain?

Back

The domain of f(x) = x^2 is all real numbers, or (-∞, ∞).

Front

Given the function f(x) = √x, what is the domain?

Back

The domain of f(x) = √x is [0, ∞) because the square root is only defined for non-negative numbers.