Piecewise Defined Functions — Unit test Answers

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches?

The graph below represents c, the amount a phone company charges, based on m, the number of minutes the customer uses each month. If there are a maximum of 44,640 minutes in a month, which equation best represents the phone company’s monthly charges?

In a certain country, a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of an ounce) has an additional cost. The function below represents the cost of mailing one letter with a weight of x ounces in this country.Josiah has two letters. The first weighs 2.9 ounces, and the second weighs 4.1 ounces. What is the total amount Josiah can expect to pay for postage?

What is the domain of the function graphed below?

What are the domain and range of the step function below?

Which of the following accurately shows the range of the function defined below?

A company manufactures 16-oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?

Which statement is true about ?

A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price number of backpacks.)

What is the vertex of the absolute value function below?

The equation of the piecewise defined function f(x) is below. What is the value of f(1)?

A city manager made the graph below to represent the number of passengers that city buses can carry, where the number of passengers is represented by x, and the number of buses by y.If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

If , what is f(5.9)?

Which piecewise relation defines a function?

A rental car company charges a base fee of $40 plus $0.25 per mile for the first 100 miles the car is driven. The company charges the same base fee plus a reduced price of $0.18 per mile for cars driven over 100 miles. The piecewise function below represents the different amounts the company charges. If someone drives their rental car 150 miles, how much will they owe the rental company?

A store offers discounts on lunch-size chip bags when buying larger quantities. The graph below represents the total cost, in dollars, for the number of bags purchased. What is the difference in the price per bag for 150 bags versus 50 bags?

A cell phone company charges by the minute (and partial minute) for making phone calls. Arionna’s plan includes 300 minutes in the $20 monthly base cost. If she uses more than 300 minutes in a month, there is a $5 overage fee and an additional charge of $0.25 per minute. Which graph represents the monthly cost, y, in dollars for making x minutes of calls?

The following graph represents dog-grooming prices at “Clean Your Paws” dog salon. If Mitzi has two dogs, a puppy that weighs 25 pounds and an adult that weighs 80 pounds, how much will it cost to bathe them both?