Domain and Range of 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

What does the vertical line test determine?

Back

It 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

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

Back

Identify the x-values for which the graph exists. The domain is the interval of these x-values.

Front

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

Back

Identify the y-values that the graph reaches. The range is the interval of these y-values.

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 an example of a function with a restricted range?

Back

f(x) = x^2, where the range is y ≥ 0.

Front

What does it mean if a function has no domain?

Back

It means there are no x-values for which the function is defined, often due to division by zero or taking the square root of a negative number.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2.

Front

What is the range of the function f(x) = x^3?

Back

The range is all real numbers, as cubic functions can produce any y-value.