Domain, Range and End Behavior of a Restricted Function

Charlotte is trying to determine the domain of a function from its equation. How can she do this?

• By finding the minimum input value.

• By analyzing the turning points of the function.

• By determining which x-values make the function undefined.

• By identifying the maximum output value.

In a math class, Charlotte is trying to understand the concept of the domain of a function. Which of the following statements about the domain of a function is accurate?

• The domain includes all real numbers unless restrictions are specified.

• The domain is always limited to positive numbers only.

• The domain is the same as the range of the function.

• The domain is determined solely by the maximum value of the function.

In a math class, Aria is trying to understand the concept of a function's range. Which of the following statements accurately describes the range of a function?

• The minimum output value of the function.

• The maximum input value of the function.

• The set of all output values that the function can produce.

• The set of all possible input values for the function.

In a math class, Aria is learning about functions. What does it mean if a function's domain is restricted?

• The function can only take negative values.

• The function will always produce a maximum output.

• The function can only take positive values.

• Certain input values are not allowed for the function.

Select TWO correct answers.

Domain

​ (a)  

Range

​ (b)  

• The domain of the function is {0,1,2,3,4,5}

• The range of the function {0,96,192,288,384,480}

• The domain of the function is all real numbers

• The domain of the function {0,96,192,288,384,480}

• The range of the function {0,1,2,3,4,5}

• The range of the function is all real numbers.

A student borrowed $480 from a friend. He agreed to make monthly payments of $96 with no interest until the loan balance was paid off. The function shown models this situation, where f(x) represents the remaining loan balance in dollars after the student has made x monthly payments. Which statements are true about the domain and range of the function for this situation? Select the correct answers.

• D: {0, 1, 2, 3, 4, 5}

• R: {0, 96, 192, 288, 384, 480}

• D: all real numbers

• R: {0, 1, 2, 3, 4, 5}

• {0, 96, 192, 288, 384, 480}

• D: {0, 96, 192, 288, 384, 480}

• R: all real numbers

Answer explanation

Domain - x values

Range - y values

Real-world examples = apply common sense and judgements

The graph shown has a domain of​ (a)   .

It has a range of (b)   ​ (c)   (d)   . ​

• ARN

• y

• >

• G

• x

• <

• E

• B

• A

• H

In a math class, Lily is trying to understand the concept of functions. She asks her teacher, "Which of the following best describes the domain of a function?"

• The set of all output values for the function.

• The set of all x-values for which the function is defined.

• The maximum value that the function can achieve.

• The minimum value that the function can achieve.

In a classroom, Rohan is trying to understand the relationship between the domain and range of a function. Which of the following best illustrates this relationship?

• The domain is always greater than the range.

• The range is a subset of the domain.

• The domain and range are always equal.

• The domain consists of input values, while the range consists of output values.

In a math class, Elijah is trying to understand what the range of a function represents. He comes across the following options:

• The set of all x-values that can be input into the function.

• The minimum input value of the function.

• The set of all values f(x) that are output for the input domain values.

• The maximum output value of the function.