Graphing Functions: Rate of Change Problems

There are a variety ways you will be asked to compare linear functions. In some cases, as in the examples below, you will be presented a series of graphs and asked to figure out which one corresponds to the question. In other cases, you will be asked to compare a linear function and a graph to determine which slope is greater.

1) For which function does the y value decrease at the slowest rate as the x value increases?

2) For which function does the y value increase at the fastest rate as the x value decreases?

 

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Answers:
  1. C
  2. B

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Explanation:

Question 1 reads: For which function does the y value decrease at the slowest rate as the x value increases? I like to focus on the X value here. If X is increasing then which direction is it moving? It is moving to the right. As the line moves to the right, what is happening to the Y value? We’re looking for a line that is sloping down (Y is decreasing) as the X is moving to the right. There are two graphs that match this scenario? Now, which of these two (C or D) has Y decreasing at the slowest rate as the X rate decreases? The answer is C because D has a steeper decreasing slope than C.

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