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

How do you determine the domain of a function given its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists.

Front

How do you determine the range of a function given its graph?

Back

The range can be determined by identifying the y-values that the graph reaches.

Front

What is an example of a function with a limited domain?

Back

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

Front

What is an example of a function with a limited range?

Back

The function f(x) = x^2 has a range of all real numbers greater than or equal to 0.

Front

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

Back

The domain is [0, ∞) because the square root function is only defined for non-negative numbers.

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.

Front

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

Back

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

Front

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

Back

The range is (0, ∞) because the exponential function is always positive.