Domain and Range

Front

What is the definition of Domain in mathematics?

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 Range in mathematics?

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 find the domain of a function?

Back

To find the domain, identify all the x-values that can be input into the function without causing any undefined situations, such as 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 y-values that result from the function's domain by evaluating the function.

Front

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

Back

The function f(x) = 1/(x-2) has a restricted domain because x cannot be 2 (it would cause division by zero). Thus, the domain is all real numbers except x = 2.

Front

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

Back

The function f(x) = x^2 has a restricted range of y ≥ 0, since squaring any real number cannot produce a negative result.

Front

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

Back

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

Front

What is the range of the function f(x) = -x^2?

Back

The range is y ≤ 0, since the function produces only non-positive values.

Front

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

Back

A function is one-to-one if each output value is produced by exactly one input value, meaning no two different x-values map to the same y-value.

Front

How can you determine if a function is one-to-one?

Back

You can determine if a function is one-to-one by using the horizontal line test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.