Uploaded by Bich Ngoc Nguyen

# MEB 2023 TUT 1

advertisement
```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 ππ(π₯π₯) and ππ(π₯π₯).
b. Write down function descriptions.
i.
iv.
ii.
ππ + ππ
v.
ππ − ππ
iii.
ππ ∗ ππ
vi.
ππ β ππ
ππ / ππ
ππ β ππ
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
ππ(π‘π‘) machine parts, where
1
ππ(π‘π‘) = 10 οΏ½π‘π‘ − 2οΏ½ = 10π‘π‘ – 5 ,
for
1
2
≤ π‘π‘ ≤ 8.
The total cost of producing x machine parts is πΆπΆ(π₯π₯) dollars, where
πΆπΆ(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 ππ(ππ) of the number d
of dollars spent on advertising, where
ππ(ππ) = 6 οΏ½1 −
200
οΏ½
ππ + 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
```