Question

iris picked a bucket of raspberries to make jam. the table shows the cups of raspberries left in the bucket, y, as a function of the number of batches of jam she makes, x. is the rate of change positive or negative? positive negative batches, x raspberries left in bucket (cups), y 1 16 4 10 7 4

Explanation:

Step1: Recall rate - of - change concept

The rate of change of a function $y = f(x)$ is given by $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. If as $x$ increases, $y$ increases, the rate of change is positive. If as $x$ increases, $y$ decreases, the rate of change is negative.

Step2: Analyze the table

When $x$ (number of batches) increases from 1 to 4 (i.e., $\Delta x=4 - 1 = 3$), $y$ (raspberries left) decreases from 16 to 10 (i.e., $\Delta y=10 - 16=-6$). The rate of change $\frac{\Delta y}{\Delta x}=\frac{-6}{3}=- 2$. Also, when $x$ increases from 4 to 7 ($\Delta x = 7 - 4=3$), $y$ decreases from 10 to 4 ($\Delta y=4 - 10=-6$), and the rate of change $\frac{\Delta y}{\Delta x}=\frac{-6}{3}=-2$.

Answer:

negative