Answers
- 1a. Graph is decreasing on the interval [tex]3 < x < 13[/tex].
- 1b. Graph is increasing on two separate intervals: [tex]0 < x < 3 \text{ and } 13 < x < 18[/tex]
- 2. Min value = 0.75, Max value = 3
- 3. Domain = [tex]0 \le x \le 18[/tex], Range = [tex]0.75 \le y \le 3[/tex]
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Explanations:
- 1a. The graph decreases whenever the curve goes downhill as you read from left to right. This is from x = 3 to x = 13. So the decreasing interval is [tex]3 < x < 13[/tex]See figure 1 below.
- 1b. The graph increases when the graph goes uphill. This happens two separate times. First from x = 0 to x = 3. Then the second portion is from x = 13 to x = 18. Refer to figure 1.
- 2. The min value is the smallest y value possible. This is y = 0.25 as shown in figure 2. This is where the lowest point on the so called "roller coaster" occurs. The max value is y = 3 which is where the highest point is located.
- 3. The domain is the set of all allowed x values. This is from x = 0 to x = 18, including both endpoints. So we say the domain is [tex]0 \le x \le 18[/tex]. The range is a similar story but for the y values. The range is [tex]0.75 \le y \le 3[/tex], which has its endpoints match up perfectly with the min and max found earlier.
