Finding Domain & 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

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers. Look for any restrictions such as holes or vertical asymptotes.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the y-values that the graph covers. Look for the highest and lowest points on the graph.

Front

What does it mean if a function has a domain of 'All real numbers'?

Back

It means that the function is defined for every possible x-value without any restrictions.

Front

What does it mean if a function has a range of 'y = 2'?

Back

It means that the output of the function is always 2, regardless of the input value.

Front

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

Back

The function f(x) = 1/x has a restricted domain because it is not defined for x = 0.

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, as it cannot produce negative values.

Front

What is the domain of the function g(m) = 25 - 2.5m?

Back

The domain is 0 ≤ m ≤ 10, as the bathtub cannot drain for negative minutes and will be empty after 10 minutes.

Front

What is the range of the function g(m) = 25 - 2.5m?

Back

The range is 0 ≤ g ≤ 25, as the bathtub starts full and can only drain to empty.