# 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?

### Click to show answers

###### Answers:

- C
- D
- A
- C
- B
- A

### Click to show explanation

###### 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).