Graphing Functions: Rate of Change Problems

Learn to compare the slopes of various graphs to determine which one is changing according to the question.

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

 

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

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

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

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

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

 

 

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Answers:
  1. C
  2. D
  3. A
  4. C
  5. B
  6. A

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Explanation:

On questions like this, focus on the X value and which way it is moving. If X is increasing then which direction is it moving? It is moving to the right.  If X is decreasing, then it is moving to the left. As the line moves to the right, what is happening to the Y value? Are we looking for Y to increase or decrease as X is moving.

  • If X is increasing and Y is increasing then the line will slope from lower left to upper right.
  • If X is increasing and Y is decreasing then the line will slope from upper left to lower right.
  • If X is decreasing and Y is increasing then the line will slope from upper left to lower right.
  • If X is decreasing and Y is decreasing then the line will slope from lower left to upper right.

There may be other trick questions like a vertical line (where slope is undefined) or a horizontal line (where Y = some number).

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