A.2A Domain & Range

Front

What is the definition of Domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the definition of Range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

Front

How do you find the domain of a function?

Back

To find the domain, identify all the values of the independent variable that can be input into the function without causing any mathematical errors (like division by zero or taking the square root of a negative number).

Front

How do you find the range of a function?

Back

To find the range, determine all the possible output values of the function by evaluating the function over its domain.

Front

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

Back

The function f(x) = 1/x has a limited domain because x cannot be 0.

Front

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

Back

The function f(x) = x^2 has a limited range of [0, ∞) because it cannot produce negative values.

Front

What does it mean for a function to be 'one-to-one'?

Back

A function is one-to-one if each element of the range is paired with exactly one element of the domain, meaning no two different inputs produce the same output.

Front

What is the relationship between the domain and range of a function?

Back

The domain consists of all possible input values, while the range consists of all possible output values that result from those inputs.

Front

How can you represent the domain and range graphically?

Back

The domain can be represented on the x-axis and the range on the y-axis of a graph, showing the relationship between inputs and outputs.

Front

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

Back

The domain is x ≥ 3, since the expression under the square root must be non-negative.