Question

Which function has the greatest rate of change.

A. y = -5x
B. { (-1,-2), (1,2), (3,6), (5,10), (7,14) }
C. A fitness club charges a $200 membership fee plus monthly fees of $25.
D. y = 3x - 16

Answer 1

Function A, represented by the equation y = -5x, has the greatest rate of change with a slope of -5, which means it changes by -5 units in the y-direction for each one unit change in the x-direction.

Step-by-step explanation:

The question asks which function has the greatest rate of change. To determine this, we compare the slope, which is the rate of change, of each function:

• Function A has a slope of -5, which means the rate of change is -5 units in the y-direction for each unit change in the x-direction.
• For Function B, the rate of change is consistent (2/1 or 2) for each x and y pair, indicating a slope of 2.
• Function C represents a linear function with a slope of 0, since the monthly fees do not change in relation to the number of months.
• Function D has a slope of 3, meaning that for each unit increase in x, y increases by 3 units.

Considering these slopes, function A has the greatest magnitude of the rate of change at -5.