Domain and Range of Functions

Front

What is the definition of 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 definition of 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

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

Given the relation (2, 3), (4, 5), (6, 7), what is the domain?

Back

The domain is {2, 4, 6}.

Front

Given the relation (1, 2), (3, 4), (5, 6), what is the range?

Back

The range is {2, 4, 6}.

Front

What is an example of a function that has a limited domain?

Back

The function f(x) = 1/x has a limited domain of all real numbers except x = 0.

Front

What is an example of a function that has a limited range?

Back

The function f(x) = x^2 has a range of all real numbers y such that y ≥ 0.

Front

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

Back

To find the domain from a graph, identify all the x-values for which there are corresponding y-values.

Front

How do you find the range of a function from its graph?

Back

To find the range from a graph, identify all the y-values that the function reaches.

Front

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

Back

The domain is x ≥ 1.