Absolute Value Functions and Transformations



2.3 Absolute Value Functions and Transformations Name

Pre-AP Algebra II Date ___________ Per ______

1. Give a verbal description of what each of the following functions would look like if graphed compared to the absolute value parent function.

[pic] [pic]

2. Write an equation in general form for the graph of the absolute value parent function given each of the following parameter changes.

Shifted 2 units down and 5 units to the right; horizontally stretched by a scale factor of 4 and reflected over the x-axis

Shifted 3 units up and 1 unit left; vertically compressed by a scale factor of ¼ and reflected over the y-axis

3. Application

Yard lines of a football field have the relationship shown in the table below (0 yard lines are the goal lines).

| | |

|Distance from one endzone|

|(yd) |

|-1 |5 |

|0 |4 |

|1 |3 |

|2 |4 |

|3 |5 |

|4 |6 |

5. At a sugar plantation processing plant, a machine fills a bag with 10 pounds of sugar. For quality control, a machine weighs each bag in ounces and rejects bags that differ from 5 pounds by more than y ounces.

a. Write an absolute value equation to show the minimum and maximum weight of sugar that could be in a bag.

b. Describe the transformation from the parent function.

6. Most cooking thermometers are accurate to within [pic].

a. If a thermometer reads [pic], write an absolute value function to determine the least and greatest possible temperatures of the meat.

b. Using a calculator, solve the equation you wrote.

c. Ham needs to reach an internal temperature of [pic] to be fully cooked. To what temperature reading should you cook a ham to ensure that the minimum temperature is reached? Explain.

7. To get a chance to win a car, you must guess the number of keys in a jar to within 5 of the actual number. Those who are within this range are given a key to try in the ignition of the car. Assume there are 596 keys in the jar. Write an absolute value inequality that describes all the possible values that will give contestants a chance to win a car.

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Football Field Yard Lines

g(x)

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