Explain the difference between a rate of change that is positive and one that is negative. Give an example of each.
Explain the difference between a rate of change that is positive and one that is negative. Give an example of each.
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Transcribed Image Text:Explain the difference between a rate of change that is positive and one that is negative. Give an example of each.
O Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with the increase in x, then the rate of change of y is positive. Whereas, if y
decreases as x increases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates, the speed increases with increasing time,
and the rate of change of its speed is positive. When the car brakes, the rate of change of its speed is negative, because the speed decreases over time.
Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with a decrease in x, then the rate of change of y is positive. Whereas, if y
decreases as x decreases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates, the speed increases, and the rate of
change of its speed is positive. When the car brakes, the rate of change of its speed is negative, because the speed decreases over time.
Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases more and more quickly as x increases, then the rate of change of y is positive.
Whereas, if y increases more and more slowly as x increases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates from a
stopped position the speed increases quickly with time, and the rate of change of its speed is positive. When the car accelerates regularly, the rate of change of its speed is negative, because
the speed increases less over time.
Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with a decrease in x, then the rate of change of y is positive. Whereas, if y
decreases as x decreases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates, the speed decreases with decreasing
time, and the rate of change of its speed is positive. When the car brakes, the rate of change of its speed is negative, because the speed increases over decreasing time.
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