2.5 Piecewise Continued

2.5 Piecewise Continued

Objective: Evaluate & Identify key features of piecewise functions.

Reminder: Key Features

• Domain: all possible x-values (beware of open circles)

• Range: all possible y- values (beware of open circles)

• Inc/Dec/Constant Intervals: tracing the graph left to right, y is either increasing, decreasing or staying constant.

• Always use parenthesis with Inc/Dec/Constant Intervals

• End Behavior: looking at 

   $\pm x$  is  $f\left(x\right)$  point towards  $\pm\infty$  

HW #5

• Domain:

   $\left(-\infty,\ \infty\right)$  

• Range:  $\left(-\infty,\ -1\right]\cup\left[1,\ 5\right]$  

• Inc Interval:  $\left(-\infty,\ -1\right)\cup\left(0,\ 2\right)$  

• Dec Interval:  $\left(-1,\ 0\right)$  

• Constant Interval:  $\left(2,\ \infty\right)$  

• As  $x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$  

Example #1

• Domain

• Range

• Inc Interval

• Dec Interval

• Constant Interval

• As $x\rightarrow\infty,\ f\left(x\right)\rightarrow\ ?$  

• Find  $f\left(-1\right)$  

Example #1

• Domain:  $\left(-\infty,\infty\right)$  

• Range:  $\left[-3,\ \infty\right)$  

• Inc Interval:  $\left(0,\ \infty\right)$  

• Dec Interval:  $\left(-1,\ 0\right)$  

• Constant Interval:  $\left(-\infty,\ -1\right)$  

• As $x\rightarrow\infty,\ f\left(x\right)\rightarrow\ \infty$  

•  $f\left(-1\right)=-2$  

Abs Value Inequalities: Word Problems

• A company that makes golf balls needs to ship bags of balls that contain 690 balls, plus or minus six balls. Write an absolute value inequality that expresses the acceptable number of balls in each bag.

• at max there can be 696 and at min there can be 684 in the bag.

• Thus, the number of balls - 690 can't be more or less than 6.

• So,  $\left|x-690\right|\le6$  

Example 1

• The average temperature in Las Vegas in July is 110 degrees. If the temperature can vary up to ten degrees. What is the inequality that represents this situation?

• at max, the temp can be 120 and at min, the temp can be 100

• Thus, the temperature - 110 has to be no more and no less than 10

•  $\left|t-110\right|<10$  

• notice, non-inclusive sign: "up to 10"

Multiple Choice

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh. Any box that varies from the weight by more than 5g is sent back. What is the inequality that shows the range of allowable weights for a box?

• $\left|w-213\right|\le5$

• $\left|w-5\right|\le213$

• $\left|w-213\right|<5$

• $\left|w-5\right|<213$

Multiple Choice

The street built in the city must be 25 ft in width with a tolerance of 0.5 ft. Streets that are not within the tolerated widths must be repaired. What is the inequality describing the situation?

• $\left|W-0.5\right|\ge25$

• $\left|W-25\right|\ge0.5$

• $\left|W-0.5\right|\le25$

• $\left|W-25\right|\le0.5$