6
QuizMultiple Choice

Analyzing Functional Relationships — Quiz

Question 6 • Algebra I

A plant food company recommends mixing a teaspoon of food with every gallon of water and only adding a teaspoon when the water level goes above the next whole gallon. Which graph models the number of teaspoons of food depending on the amount of water?

Answer
A
Image with description On a coordinate plane, the x-axis ranges from 0 to 6 in increments of one-half, and the y-axis ranges from 0 to 5 in increments of one-half. A segment goes from a closed circle at the point 1 comma 1 to a closed circle at the point 2 comma 1. A second segment goes from an open circle at the point 2 comma 2 to a closed circle at the point 3 comma 2. A third segment goes from an open circle at the point 3 comma 3 to a closed circle at the point 4 comma 3. A fourth segment goes from an open circle at the point 4 comma 4 to a closed circle at the point 5 comma 4. A fifth segment goes from an open circle at the point 5 comma 5 to a closed circle at the point 6 comma 5.
B
Image with description On a coordinate plane, the x-axis ranges from 0 to 5 in increments of one-half, and y-axis ranges from 0 to 5 in increments of one-half. A straight line originates from 0 comma 0, and goes to the right passing through the point 5 comma 5.
C
Image with description On a coordinate plane, the x-axis ranges from 0 to 5 in increments of one-half, and the y-axis ranges from 0 to 5 in increments of one-half. A segment goes from an open circle at the point 0 comma 5 to a closed circle at the point 1 comma 5. A second segment goes from an open circle at the point 1 comma 4 to a closed circle at the point 2 comma 4. A third segment goes from an open circle at the point 2 comma 3 to a closed circle at the point 3 comma 3. A fourth segment goes from an open circle at the point 3 comma 2 to a closed circle at the point 4 comma 2. A fifth segment goes from an open circle at the point 5 comma 1 to a closed circle at the point 5 comma 1.
D
Image with description On a coordinate plane, the x-axis ranges from 0 to 5 in increments of one-half, and y-axis ranges from 0 to 5 in increments of one-half. A straight line originates from 0 comma 5, and goes to the right to the point 5 comma 0.

Explanation

The amount of food stays constant until the water level goes above the next whole gallon. For example, 1 teaspoon is used from 1 gallon through exactly 2 gallons; once the water exceeds 2 gallons, the amount becomes 2 teaspoons. The steps in choice A show this pattern, with each new step beginning just above a whole-gallon mark.

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