Domain and Range from Word Problems

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 (usually x) that will not cause any undefined behavior in the function.

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 (usually y) that result from substituting the domain values into the function.

Front

In the context of a word problem, how do you determine the domain?

Back

To determine the domain, identify the constraints on the independent variable based on the context of the problem, such as physical limitations or specified conditions.

Front

In the context of a word problem, how do you determine the range?

Back

To determine the range, calculate the output values of the function based on the identified domain values and any constraints given in the problem.

Front

What is the domain of the function y = 3x when x is between 25 and 30?

Back

The domain is {25, 26, 27, 28, 29, 30}.

Front

What is the range of the function y = 3x when x is between 25 and 30?

Back

The range is {75, 78, 81, 84, 87, 90}.

Front

If a car travels 25 miles per gallon and can hold 14 gallons, what is the maximum distance it can travel?

Back

The maximum distance is 25 miles/gallon * 14 gallons = 350 miles.

Front

What is the domain of the function f(x) = 40 + 10x for x representing months in a gym membership?

Back

The domain is x ≥ 0, representing the number of months.

Front

What is the range of the function f(x) = 40 + 10x for x representing months in a gym membership?

Back

The range is $40, $50, $60, ..., representing the total cost.

Front

In the equation f(x) = 30 + 12.5x, what does x represent?

Back

In this equation, x represents the number of people ordering meals.