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) = √(x - 1).

Back

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

Front

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

Back

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

Front

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

Back

The domain is all real numbers except x = 3, which makes the denominator zero.

Front

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

Back

The range is all real numbers except y = 0, as the function approaches but never reaches zero.

Front

Identify the domain of the function f(x) = log(x).

Back

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

Front

Identify the range of the function f(x) = log(x).

Back

The range is all real numbers, as the logarithm can take any value from negative infinity to positive infinity.

Front

What is the domain of the function f(x) = sin(x)?

Back

The domain is all real numbers, as the sine function is defined for all x.

Front

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

Back

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