Domain and Range

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

Identify the domain of the function: f(x) = 1/(x-2)

Back

The domain is all real numbers except x = 2, or in interval notation: (-∞, 2) ∪ (2, ∞).

Front

Identify the range of the function: f(x) = x^2

Back

The range is [0, ∞) since the output of x^2 is always non-negative.

Front

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

Back

It means the domain of the function is (-∞, ∞).

Front

Find the domain of the function: f(x) = √(x-1)

Back

The domain is [1, ∞) because the expression under the square root must be non-negative.

Front

Find the range of the function: f(x) = -x^2 + 4

Back

The range is (-∞, 4] because the maximum value occurs at x = 0.

Front

What is the domain of the function: f(x) = log(x)

Back

The domain is (0, ∞) since the logarithm is only defined for positive numbers.

Front

Identify the range of the function: f(x) = sin(x)

Back

The range is [-1, 1] since the sine function oscillates between -1 and 1.

Front

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

Back

The domain is all real numbers except x = 0, or in interval notation: (-∞, 0) ∪ (0, ∞).