1.2 Lesson 12 Relating Key Features to Real World Contexts

Open Ended

Explain why the value (30, -10) does not make sense in the context of Antonella's smoothie purchases.

Multiple Choice

What is the domain and range for the amount of money Antonella has remaining after buying smoothies with her $65 gift card?

• 0 ≤ x ≤ 26 and 0 ≤ y ≤ 65

• 0 ≤ x ≤ 30 and 0 ≤ y ≤ 65

• 0 ≤ x ≤ 26 and -10 ≤ y ≤ 65

• 0 ≤ x ≤ 30 and -10 ≤ y ≤ 65

Multiple Choice

What does it mean for the domain and range of a linear function to be viable or nonviable?

• Viable values are realistic and possible in the context; nonviable values are not possible or do not make sense.

• Viable values are always positive; nonviable values are always negative.

• Viable values are always integers; nonviable values are always fractions.

• Viable values are always increasing; nonviable values are always decreasing.

Multiple Choice

When modeling the number of cars that can be parked in a parking lot, what are the only viable types of numbers for both the domain and range?

• Positive whole numbers

• Negative numbers

• Fractions

• Any real number

Multiple Choice

Given the function A(c) = 20 - 2.75c representing the amount of money left on a gift card after buying c cups of coffee, what is the maximum number of cups Bella can buy before running out of money?

• 7

• 7.27

• 8

• 6

Multiple Choice

What is the slope of the function A(c) = 20 - 2.75c, and what does it represent in the context of the gift card scenario?

• 2.75; the amount added to the card per cup of coffee purchased

• -2.75; the amount subtracted from the card per cup of coffee purchased

• 20; the starting value of the card

• 0; the card balance never changes

Open Ended

Explain what the y-intercept (0, 20) indicates about the gift card in the function A(c) = 20 - 2.75c.

Multiple Select

Which of the following statements about the domain of the function A(c) = 20 - 2.75c are correct?

• The domain should only include whole numbers because you can't buy a fraction of a cup of coffee.

• The domain can include negative numbers because you can owe coffee.

• The domain is limited to positive numbers because you can't buy negative cups of coffee.

• The domain can include decimals because the function is continuous.

Multiple Choice

After how many cups of coffee will the gift card balance reach $0 according to the function A(c) = 20 - 2.75c?

• 2.75

• 7.27

• 20

• 0

Multiple Choice

Given the function P(x) = -1.7x + 74.5, where x is the number of years since 1998, what does the y-intercept represent in this context?

• The percentage of companies that performed drug tests in 1998.

• The number of companies that stopped drug testing in 1998.

• The year when drug testing started.

• The rate at which drug testing decreased each year.

Open Ended

What questions do you still have about determining the domain and range of a function from a real-world context?

Open Ended

Determine if the key features given by Li Qiang for the equation W(x) = 3x + 8 are viable for the context of marbles in a container. If a feature is not viable, explain why.