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 of a function, identify all the values of the independent variable that do not cause the function to be undefined, such as avoiding 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 of a function, determine all the possible output values 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-2) has a limited domain because x cannot equal 2, as it would make the denominator zero.

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 the output values (y) are always non-negative.

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 vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve at more than one point, the curve is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

Front

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

Back

The domain of f(x) = √(x-1) is [1, ∞) because the expression under the square root must be non-negative.