MAT171 Practice Exam(1)

MAT 171 Final Exam Review Questions – Practice Test
*note, this has more questions than a typical Final Exam so it should take you longer.
1. Given the functions f(x) = x 2 − 9 and g(x) = √5 − x, find the following:
a. (f ∘ g)(x)
b. Domain of (f ∘ g)(x)
c. ( g f ) (x)
d. Domain of ( g f ) (x)
2. Determine the quotient and remainder of the division: 5x3 +41x 2 +30x−1
x 2 +7x−2
Quotient: _____________
Remainder: _____________
3. The anti-bacterial effectiveness of new surface material coatings is being studied in a lab testing to
see if it can slow the growth of bacteria on a surface over time. Scientists start the experiment with
45 bacteria cells on the surface product. The bacteria seem to be doubling every 4 hours.
Approximately how long will it take for there to be 1200 bacteria cells?
4. Solve: log 4 (x + 2) + log 4 (x − 4) = 2

5. Given the piecewise graph h(x) below, find the following:
a. Intervals of decrease:
b. When h(x) < 0
c. Domain:
d. Range:
e. h(−3)
6. Given the function y = x2 +3x−28
, find the following:
2x 2 −13x+20
a. Vertical asymptote(s): ____________________________
b. Hole(s): ________________________________________
c. Domain: ________________________________________
d. X-intercept(s): ___________________________________
e. Y-intercept: _____________________________________
7. Simplify the expressions:
a. (−3√−49 + 18) − 2(5 + 9i) + 4i 2
b. (6 − 8i)(−7 + 2i)
c. (x − (4 + 2i))(x − (4 − 2i))
8. Describe the function transformations that have been applied to y = x 2
to give f(x) = −2 + 3(x + 7) 2 .

9. The function g(x) = (x − 3) 2 + 8 has a domain restriction of x ≥ 3.
Find g −1 (x) and describe its domain.
10. Write the equation of the function graphed below:
11. Solve the equation: −6|10 + 2x| − 5 = −17
12. Find the difference quotient of the function f(x) = 3x 2 − 11x + 8

13. Match the horizontal asymptote with the rational function. (some answer choices may be used
more than once or not at all)
___ y = x2 −2x+1
x 2 −4
___ y = 4x−9
2x+6
___ y = 2x3 +3x 2 −9x−23
x 2 −5
___ y =
25−x2
x 2 +6x+5
___ y = 5x2 +34x+33
5x+4
___ y = −1
x+8
a. y = 0
b. y = −1
c. y = 1
d. y = −2
e. y = 2
f. y = 2x + 3
g. y = 5x + 4
h. y = x − 8
i. y = x + 6
j. y = 2x − 8
k. y = −4x + 9
___ y =
−2x+7
x 2 +13x+7
14. Newton Banking & Trust if offering a savings account with a 3.14% interest rate. If your principal
investment is less than $10,000 then the account will be compounded continuously. If your
investment is over $10,000, the account will be compounded quarterly.
René decides to open an account and invest $9500. Blaise also opens an account but invests
$10,400.
If they both leave the money in the accounts for 10 years, which person will have more money?
How much more?
15. Solve the inequality and write the solution in interval notation: 4x 2 + 8 ≤ 33x

16. An amusement park charges $18 for each adult ticket and $7 for each child ticket. One day the park
earned $4,120 in ticket sales. Let x represent the number of adult tickets sold. Let y represent the
number of child tickets sold. If 400 tickets were sold on this day, how many of them were adult
tickets and how many were child tickets?
17. Use the function h(x) = −2x 2 + 20x − 37 to determine the following:
a. Does the function have a maximum or a minimum?
b. What is the vertex of the function?
c. What is the axis of symmetry?
d. What is the y-intercept?
e. Determine the type of roots the function will have:
2 imaginary roots 2 real roots
1 imaginary root, 1 real root 1 real root
18. Use the polynomial P(x) = x 3 − 11x 2 − 13x + 87 to determine:
a. Which of the following is a zero of the polynomial: x = 5, x = −1, x = −3
b. Find all the remaining zeros.
19. A company found that its monthly profit, P, is given by the function
P(x) = −10x 2 + 120x − 150 where x is the selling price for each unit of the product.
a. What is the expected profit if the company charges $8.75 for each unit?
b. What price should the company set for the product so that it reaches a maximum profit?
c. At what price(s) would the company expect to make no money at all?

20. Solve: 5x 3 − 4 = x 2 − 20x
21. Iodine-131 is a radioactive substance that can be used to treat certain thyroid conditions. It has a
half-life of 8 days. Your friend with a thyroid condition is given 40 mg of I-131 to drink.
a. How much will remain after 32 days?
b. Approximately when will there be 15mg of I-131 in her body?
22. In the function f(x) = a√x + b + c, match the following:
___ What happens to the graph when the value of “a” increases?
___ What happens to the graph when the value of “b” increases?
___ What happens to the graph when the value of “c” decreases?
a. Function shifts up
b. Function shifts down
c. Function shifts left
d. Function shifts right
e. Vertical stretch
f. Vertical shrink
g. Horizontal stretch
h. Horizontal shrink
i. Reflection over the x-axis
j. Reflection over the y-axis
23. Write the form of the partial fraction decomposition of the rational expression
−4x+18
x 2 −12x+35

24. Use the polynomial graph below to describe the following key features:
a. Locate all local maximum and local
minimum (estimate if needed).
b. List the zeros of the polynomial and
their multiplicities?
c. Describe the domain and range of the
polynomial?
d. Describe the end behavior of the
polynomial:
As x → −∞, f(x) → ______
As x → ∞, f(x) → ______
25. Solve and write your solution in interval notation: −3(x + 6) 2 (x − 1)(x − 4) 3 ≤ 0
26. Solve and simplify, showing all work: 5 3x−9 = 10 7x+2

27. Write the equation of the rational function graphed below. Explain how you determined the
equation using the graph’s key features:
28. Solve: x−5
x−2 =
3x−3
x 2 +2x−8 + 1
29. Solve the system, showing all work: x2 + y 2 = 29
x − y = −7

30. The function f(x) is graphed below. Compute the average rate of change in f as x increases from
-1 to 8.