MEB 2023 TUTORIAL 1 FUNCTIONS Question 1: Decide which curves are graphs of functions. a. b. c. d. e. f. Question 2: a. Find f (0) and f (7). b. Is f (4) positive or negative? c. For what values of x is f ( x) ≤ 0 c. For what values of x is f ( x) = 0 . Question 3: Find the domain and the range of the following functions. 1. ) f ( x= 4 − 9 x2 2. f ( x) = 2 x − 5 − 1 4. f ( x) = 1 x +3 5. f ( x) = 3 x 3. f ( x) = x 2 + x + 3 6. x2 + x + 1 f ( x) = x +1 1|Page MEB 2023 Question 3: In the following problems, an equation involving x and y is given. For each problem, determine whether y is a function of x. If it is a one-to-one function, please specify and explain. If it is a function, find the domain and range. 1. y − 2 = 2 x + 4 2. x 2 − y = 3 3. 4. y + 1 + x = 3 3. y − x + 2 − 2 = 2x 4. y − x 2 − 2 x − 4 = 0 Question 4: Find the inverse of the following functions. x +1 1. f (= 2. f ( x) = x) 2 x − 2 x −1 2 Question 5: Let f ( x= ) x + 1 and g ( = x) x −1 . x + 3 − y2 +1 = 0 3. f ( x= ) 2 x −1 − 2 a. Find domains and ranges of ππ(π₯π₯) and ππ(π₯π₯). b. Write down function descriptions. i. iv. ii. ππ + ππ v. ππ − ππ iii. ππ ∗ ππ vi. ππ β ππ ππ / ππ ππ β ππ Question 6: In 2022, a patient paid $700 per day for a semiprivate hospital room and $1900 for an appendectomy operation. a. Express the total amount paid for an appendectomy as a function of the number of days of hospital confinement. b. Calculate the number of days of hospital confinement if the patient has spent $4700. Question 7: 1. During the first 1/2 hours, the employees of a machine shop prepare the work area for the day’s work. After that, they turn out 10 precision machine parts per hour, so the output after t hours is ππ(π‘π‘) machine parts, where 1 ππ(π‘π‘) = 10 οΏ½π‘π‘ − 2οΏ½ = 10π‘π‘ – 5 , for 1 2 ≤ π‘π‘ ≤ 8. The total cost of producing x machine parts is πΆπΆ(π₯π₯) dollars, where πΆπΆ(π₯π₯) = 0.1π₯π₯ 2 + 25π₯π₯ + 200. a. Express the total cost as a (composite) function of t. b. What is the cost of the first 4 hours of operation? 2|Page MEB 2023 2. The revenue π π (π₯π₯) (in thousands of dollars) that a company receives from the sale of x thousand units is given by π π (π₯π₯) = 5π₯π₯ − π₯π₯ 2 . The sales level π₯π₯ is in turn a function ππ(ππ) of the number d of dollars spent on advertising, where ππ(ππ) = 6 οΏ½1 − 200 οΏ½ ππ + 200 Express the revenue as a function of the amount spent on advertising. Question 8: A streaming service that offers a basic plan for $10 a month with 100 hours of streaming included. Beyond the 100 hours, the company charges $0.05 per hour. a. Write the function describing the streaming policy. b. Find the cost for streaming 250 hours in a month. 3|Page