Question

mathematics ii a trayer fall 25 analyzing functional relationships 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?

Explanation:

Step1: Understand the problem

The company recommends 1 teaspoon per gallon, and add a teaspoon only when water level exceeds the next whole gallon. So the number of teaspoons \( y \) is the floor function of the water amount \( x \) (or a step function increasing by 1 at each integer \( x \), with open circles at the integers and closed circles at the next point).

Step2: Analyze the graphs

• The first graph (top) has vertical segments with open circles at the start of each segment (e.g., at \( x = 1, 2, \dots \)) and closed circles at the end, increasing by 1 each time, which matches the step - by - step addition (add 1 tsp when water > 1 gal, > 2 gal, etc.).
• The second graph is a linear line, which would imply a continuous addition (e.g., 0.5 tsp for 0.5 gal), which doesn't match the "add only when water level goes above the next whole gallon" rule.
• The third graph is a decreasing line, which is opposite to the relationship (more water should mean more or equal teaspoons, not less).
• The fourth graph is decreasing in steps, which also doesn't match as we need an increasing step function.

Answer:

The first graph (the top - most graph with the vertical red segments and open/closed circles) models the number of teaspoons of food depending on the amount of water.