# QCC MA-119 Final Review Questions. HSI QCC MA-119 Spring 2021 Final Review Questions Page 1 of 12 Graphs and Functions 1. Use the graph of the function, ? = ?(?), to answer the question. a) Estimate...

QCC MA-119 Final Review Questions.
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 1 of 12

Graphs and Functions
1. Use the graph of the function, ? = ?(?), to answer the question.
a) Estimate ?(1)
Answer: ?(1) ≈ 5 (find a point on the graph that has ?-coordinate = 1).
b) Estimate the solution(s) to ?(?) = 9
Answer: ? ≈ 1.75 (find all points on the graph that have ?-coordinate=9; in this case,
there's just one such point).
c) Estimate the coordinates of all intercepts.
Answer: ?-intercept is approximately(−8.5,0). (All ?-intercepts have ?-coordinate=
0.) There’s only one ?-intercept in this graph; ?-intercept is approximately(0,3). (All ?-
intercepts have ?-coordinate= 0. There’s only one y-intercept in this graph.)
d) Estimate the domain and range of the function
Answer: Domain: (−∞, ∞). (The arrows indicate that the graph extends, without
breaks, indefinitely to the left and indefinitely to the right.) Range: (−∞, ∞). (The
arrows indicate the graph extends, without breaks, indefinitely up and indefinitely
down.)
e) Estimate the minimum or maximum ?-value
Answer: no minimum ?-value and no maximum ?-value. (The arrows indicate that the
graph extends indefinitely up and indefinitely down.)
f) Estimate the ?-value at which the minimum or maximum is achieved?
g) Estimate the values of ? for which ? < 0
Answer: (−∞, 8.5) For these ?-values the graph is below the ?-axis so for these ?-
values, ?<0. See how this answer relates to part c)
h) When 1 < ? < 2, is the function increasing or decreasing?
Answer: Increasing. Move to the right within the stated interval of ?-values. The graph
is going upwards for those ?-values.

2. Use the graph of the function, ? = ?(?), to answer the question.
a) Estimate ?(−11)
Answer: ? = ?(−11) ≈ 7
b) Estimate the solution(s) to ?(?) = −4
Answer: ? ≈ −13 and ? ≈ −6
c) Estimate the coordinates of all intercepts.
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 2 of 12

Answer: ?-intercepts: (−14,0), (0,0), (9,0); ?-intercept: (0,0)
d) Estimate the domain and range of the function
Answer: Domain (−∞, ∞) Range [−7.75, ∞)
e) Estimate the minimum or maximum ?-value
Answer: minimum ?-value ≈ −7.75; no maximum ?-value
f) Estimate the x-value at which the minimum or maximum is achieved?
Answer: For minimum: ? ≈ −10 (The ?-coordinate of the point with the minimum ?-
value); For maximum: no such ?-value
g) Estimate the values of ? for which ? < 0
Answer: (−14,0) ∪ (0,9) (the symbol ∪ stands for union or “together with”. The
endpoints are not included because there we have ? = 0 not ? < 0
h) When 4 < ? < 5, is the function increasing or decreasing?
3. Compute
?(4)−?(1)
4−1
for the given function.
a) ?(?) = ?2 − 3? + 1
b) ?(?) = √?
1
3

Linear Functions
4. Suppose that a manufacturer wishes to use a linear function to model how the demand for its
product affects the product’s price. The unit price function has the form ?(?) = ?? + ? where
? is the number of units of the product in demand. Suppose that when 2400 units are
demanded then the unit price is \$250 and when 3000 units are demanded then the unit price
is \$300.
Number of units ? Price per Unit ?
XXXXXXXXXX
XXXXXXXXXX
a) Determine the equation of the function ?(?) = ?? + ?
b) According to this model, what is the unit price ?(?) if the demand is ? = 3600?
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 3 of 12

1
12
? + 50 b) \$350
5. A linear function ? passes through (−1,5) and (2, −4). Find the function value ?(−2).
6. Markos currently has 200 songs in his music collection. Every month, he adds 15 new songs.
Write a formula for the number of songs, ?, in his collection as a function of time, ?, the
number of months. How many songs will he own in a year?
Answer: ?(?) = 15? + 200; 380 songs
7. A town’s population has been growing linearly. In 2004 the population was 6,200. By 2009
the population had grown to 8,100. Assume this trend continues.
a) Write a linear equation to model the population growth.
Answer: ?(?) = 380? + 6200, where ? is the number of years since 2004.
b) Predict the population in 2013.
c) Identify the year in which the population will reach 15,000.
Answer: Sometime around the year 2027
8. Factor completely. 40?4 + 22?3 − 6?2
Answer: 2?2(4? + 3)(5? − 1)
a) 4?2 + ? = 3
Answer: ? = −1 or ? = −
3
4

b) (? + 1)(? − 3) = 2
Answer: ? = 1 ± √6
c) ?2 + 7? + 12 = 0
Answer: ? = −3 or ? = −4
d) 2?2 + 1 = ?
1±?√?
4

e) 2(? XXXXXXXXXX = 0
Answer: ? = −3 ± 2?
f)
1
3
?2 + ? = −
1
2

−3±√3
2

g) 4?2 − ? − 3 = 0
Answer: ? = 1 or ? = −
3
4

h) (? −
1
3
)
2

4
9
= 0
Answer: ? = 1 or ? = −
1
3

HSI QCC MA-119
Spring 2021 Final Review Questions
Page 4 of 12

10. Graph the following quadratic functions.
a) ?(?) = −?2 − 6? − 5
b) ℎ(?) = −(? − 3)(? + 2)
c) ?(?) = 2?2 − 3? − 2
d) ?(?) = −2?2 − 4? + 5
e) ?(?) = (2? − 1)(? + 3)
f) ?(?) = 2?2 + 8
Before graphing the parabolas, state which open upwards and which open downwards.
For each parabola include
a) The coordinates of all intercepts
b) The coordinates of the vertex
c) The equation and graph of the axis of symmetry
d) The domain and range in interval notation
e) The coordinates of an additional point on the graph
f) The maximum or minimum range value
g) The domain value at which the max or min is reached
h) ?-interval(s) at which the function is negative
i) ?-interval(s) at which the function is positive
11. The length of a rectangle exceeds twice its width by 3 inches. If the area is 10 square inches,
find the rectangle's dimensions. Round to the nearest tenth of an inch.
Answer: Approximately 1.6 in by 6.2 in.
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 5 of 12

12. The hypotenuse of a right triangle is 6 feet long. One leg is 2 feet shorter than the other. Find
the lengths of the legs. Round to the nearest tenth of a foot.
Answer: Approximately 5.1 ft and 3.1 ft.
13. A retailer estimates that, by charging x dollars each for a particular phone case, she can sell
40 − ? units each week. The function ?(?) = ?(40 − ?), models the weekly revenue, ?(?),
received when the selling price is ?.

a) Interpret (0, ?(0)) and (1, ?(1)) in context.
Answer: When the charge is \$0, the revenue is \$0; When the charge is \$1, the revenue
is \$39
b) Find the selling price that will give the maximum revenue, and then find the amount of
the maximum revenue.
Answer: The maximum revenue is \$400 when the charge is \$20
c) For which selling price(s) will the weekly revenue equal \$300?
14. A ball is thrown vertically upward, at the rate of 120 ft/sec, from a rooftop with a height of 50
feet. The quadratic function ℎ(?) = −16?2 + 120? + 50 models the height of the ball, from the
ground, at time ?.

a) Interpret (0, ℎ(0)) and (1, ℎ(2)) in context.
Answer: 0 seconds after the ball is thrown the ball is 50 feet from the ground; 1
second after the ball is thrown the ball is 154 feet from the ground.
b) Find how long it will take the ball to reach its maximum height, and then find the
maximum height.
Answer: The maximum height of 275 feet is reached in 3.75 seconds
c) At which time(s) does the ball reach 200 feet above ground?
d) When does the ball hit the ground?
15. Find the domain of the following functions.
a) ?(?) =
?
?−3
− 2
Answer: (−∞, 3) ∪ (3, ∞)
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 6 of 12

b) ?(?) = 1 − √3? − 6
16. Given functions ?(?) = √? − 3, find:
a) ?(7) − 2
b) the domain of the function ? which is define as ?(?) = ?(?) − 2.
17. Simplify the following rational expression.
a)
?
?+2
+
2
?−4

?2−2?+4
(?−4)(?+2)

b)
4
?

3
?−5
+
5
?+3

6(?2−7?−10)
?(?−5)(?+3)

c)
?+2
?+8

18
?2+13?+40

?−1
?+5

d)
1
3+ℎ

1
3

1
3(3+ℎ)

18. Solve for ? from the following equation.
a) ? =
?−2
?+3

3?+2
?−1

b) ? = √3? + 10
c) ? − √3? − 2 = 4
d)
?+2
?+1
+
5
?2+4?+3
− 1 = 0
Answer: ? = −8 (from linear)
e)
?2
?−3
+ 2 =
12−?
?−3

Exponential and Logarithmic Functions
19. Solve for ? to the nearest hundredth from: ln(2? + 1) = 5.
20. The value V of a car measured in dollars, is given by the formula: ? = 40, XXXXXXXXXX)−0.4?
where ? is the age of the car in years. Find the age of the car, to the nearest hundredth of a
year, when the value of the car will be \$20,000.
21. Solve to the nearest hundredth: ?2? = 7 . Answer x ≈ 0.97
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 7 of 12

22. Solve to the nearest tenth: 5 ?−3? = 2 . Answer ? ≈ 0.3 .
23. The function ?(?) = 70?3/4 models the number of calories per day, a person needs to
maintain life in terms of that person's weight, ?, in kilograms. (?=person's weight; ?(?) =
calories needed).
a) If a person weighs 80 kilograms, how many calories per day does this person need to
b) Mark a point on the graph that conveys the information from part (a). (The graph was
given in the Review sheet).
Answer: Mark the point (80, ?(80)) or (80,1872.47)

24. Solve for ? to the nearest hundredth: 32?+1 = 38.
25. Marcel deposits \$9,000 in a bank that gives an annual interest rate of 4 .25% per year, which
is compounded quarterly. What will his balance be after 10 years?
26. Consider the logarithmic function ?(?) = log7? + log7(? − 6). Find the value of x such that
?(?) = 1.
Answer: ? = 7 (It’s a coincidence that the answer matches the base); reject ? = −1
27. Solve for the exact value of ? from: log27?
2 − log27? = 2/3.
28. Solve for the exact value of ? from: 41−3? = 1
1
3

29. Mike invests \$6,700 at 5.1% annual interest compounded monthly. He wants to know how
long he should invest the money for his investment to triple in value. You may use the
formula ? = ?(1 +
?
?
)??. Round to the nearest hundredth.
30. Find the domain of the function: ?(?) = ln(5 − 3?). Express your answer in interval notation.
5
3
)
31. Solve for ? from: log4? + log4(? − 6) = 2 by
a) finding an equivalent equation without logarithms,
Answer: ?(? − 6) = 42
b) and solving this equation.
Answer: ? = 8; reject ? = −2
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 8 of 12

32. Solve for ? from: log(16 − 20?) − log(−?) = 2
1
5

33. The amount ? in grams, of a radioactive material remaining after t days is given by ? =
100?−0.004?. Find the number of days, to the nearest hundredth, when there will be 60 grams
left.
Absolute Value Functions
34. Consider the function ?(?) = 3|2? − 5| − 4. Find all values of ? for which ?(?) = 5. Write
35. Consider the function ?(?) = −2|4? − 3| + 7. Find all values of ? for which ?(?) = −3. Write
1
2
, 2}
Slopes of parallel/perpendicular lines
36. Write the equation of the line passing through (−2,3) and parallel to the line 3? − 2? = 5.
3
2
? + 6
37. Write the equation of the line that passes through (−6,7) and perpendicular to the line that
has ?-intercept of 2 and ?-intercept of −4. Express your answer in the slope-intercept form.
1
2
? + 4
38. Let ?1 be a line whose equation is 5? + 3? = 6 and ?2 be a line that passes through the points
(−2,0) and (3, −6). Determine if the lines ?1 and ?2 are parallel, perpendicular or neither.
Linear Inequalities and Interval Notations
39. Solve the following inequalities. Use interval notation to express the solution sets.
a) 1 −
1
3
(2? + 5) ≥ 2 − 6?
1
2
, ∞)
b) −3 ≤
2?−1
3
< 5
c) −6 ≤
−2?−4
2
< −3
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 9 of 12

Radicals, Rational Exponents and Complex Numbers
40. Simplify. Express your results with positive exponents only.
(
?
5
2?−5
27?−
1
2?
)

2
3

9?4
?2

a) (
?

1
3
√?2
3 )
−3

b) (?−3?
1
2)
2
3

√?
3
?2

c) √48x8y
5

d) √8?4
3
− 8√?7
3

3

e) √27?9
3
+ √?6
3

f)
√?
1−√?

?+√?
1−?
.
42. Evaluate the polynomial ?2 − 3? + 5 at ? = 1 + ?. Express your answer in the form ? + ??.
43. Evaluate the expression ?2 + 5? − 3? when ? = −3 + 4?. Express your answer in the form ? +
??.
44. Show whether x = 1+2i is a solution of ?2 − 2? + 5 = 0 .
45. Solve ?2 + 9 = 0 for the complex number z. Answer z = +3i or Z=-3i.
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 10 of 12

Geometric problems
46. Use basic geometry is used to set up a quadratic equation and solve the problem.
a) A circle is inscribed in a square as shown. The area of the square is 16 cm2. Find the
16−4?
4
≈ 0.86 cm2
b) A circle is inscribed in a square as shown. The two shown diameters are
perpendicular. The area of the circle is 10 cm2. Find the length of the dashed line
segment.
20
?
≈ 2.52 cm
c) The area between two concentric circles is 25 cm2. The radius of the outer circle is 1
cm more than the radius of the inner circle. Find the length of each radius.
25−?
2?
≈ 3.48 cm. The radius of the outer
circle is
25+?
2?
≈ 4.48 cm.
HSI QCC MA-119
Spring 2021 Final Review Questions
Page 11 of 12

d) A circle is inscribed in a square as shown. The two shown diameters are
perpendicular. The side of the square is 10 cm . Find the area of the shaded region.
e) A rectangle is shown inscribed in a circle. The rectangle’s diagonals bisect each other
at the circle’s center. The area of the circle is 16 π cm2. The length of ?? is 3. Find the
length of the segment ??.
Answer: ?? = √??2 − ??2 = √4?2 − 9 = √64 − 9 = √55 cm.

HSI QCC MA-119
Spring 2021 Final Review Questions
Page 12 of 12

Graph the quadratic functions ?(?) = −2?2 − 4? + 5
Without graphing, we know the parabola will open downwards because ? = −2 < 0 (a is the
a) The coordinates of all intercepts
b) The coordinates of the vertex
c) The equation and graph of the axis of symmetry
Answer: shown on graph; ? = −1
d) The domain and range in interval notation
e) The coordinates of an additional point on the graph
f) The maximum or minimum range value
g) The domain value at which the max or min is reached
h) ?-interval(s) at which the function is negative
−2−√14
2
) ∪ (
−2+√14
2
, ∞) ≈ (−∞, −2.871) ∪ (0.871, ∞)
i) ?-interval(s) at which the function is positive
−2−√14
2
,
−2+√14
2
) ≈ (−2.871,0.871)
Answered 9 days AfterMay 11, 2021

## Solution

Himanshu Sahni answered on May 21 2021

og ng(x3 )= /
x(-3)...

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