MATH 1201-01 / MATH 1201 Assignment Unit
3 | Bungee Jump, Road Planning &
Electricity Pricing | Complete Solutions |
2026/2027 Updated | University of the People
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
97 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
Assignment Unit 3 of MATH 1201 College Algebra applies function concepts to real-world modeling tasks
including bungee jump height, road planning with polynomial curves, and electricity pricing with rational and
exponential functions. The exam assesses domain/range, rates of change, composition, transformations,
inverse functions, and asymptotic behavior through multi-step algebraic reasoning.
STUDY GUIDE
Recommended duration: 3 hours. Passing target: 70% (C or better).
HIGHP - Page 1 of 31
,1. A bungee jumper's height above ground is modeled by h(t) = 50 + 30cos(t/2) for t 0.
What is the exact time in the first cycle when the jumper is momentarily at the lowest
point, and what is that minimum height?
[ ] A. t = 1 s; h = 20 m
[ ] B. t = 2 s; h = 20 m
[ ] C. t = 1 s; h = 80 m
[ ] D. t = 2 s; h = 80 m
CORRECT: B. t = 2 s; h = 20 m
The cosine term reaches its minimum value of 1 when t/2 = , giving t = 2 s. Substituting yields h = 50 + 30(1)
= 20 m. Options A and C misplace the time; D gives the maximum height, not the minimum.
2. A road curve is designed so its elevation follows P(x) = 0.02x³ + 0.3x² + 1.5x + 2 for 0 x
10 (x in hundreds of meters). Which statement correctly describes the end behavior of P(x)
as x -> ?
[ ] A. P(x) -> because the quadratic term dominates.
[ ] B. P(x) -> because the cubic term dominates.
[ ] C. P(x) -> 0 because the constant term dominates.
[ ] D. P(x) oscillates without limit due to the cubic term.
CORRECT: B. P(x) -> because the cubic term dominates.
For a cubic with negative leading coefficient, as x -> the leading term 0.02x³ dominates and drives P(x) -> .
The quadratic term is lower degree and cannot control end behavior; polynomial functions do not oscillate.
3. An electricity company charges C(k) = 0.12k + 15 for 0 k 500, and C(k) = 0.25k 50 for k
> 500 (k in kWh). What is the domain of the inverse function that gives kWh as a function
of cost for the first tier?
[ ] A. 0 C 75
[ ] B. 15 C 75
[ ] C. 0 C 500
[ ] D. 15 C 500
CORRECT: B. 15 C 75
For the first tier, k [0, 500] maps to C(0) = 15 and C(500) = 75. The inverse's domain is the range of the
original function on that interval, i.e., [15, 75]. Options A and D confuse the input and output intervals; C uses
the kWh range instead of the cost range.
HIGHP - Page 2 of 31
,4. Let f(x) = (x 3) and g(x) = x² + 1. What is the domain of (f g)(x)?
[ ] A. All real numbers
[ ] B. x 3
[ ] C. x 2 or x 2
[ ] D. x 2
CORRECT: C. x 2 or x 2
Compute (f g)(x) = (x² + 1 3) = (x² 2). The radicand must be nonnegative: x² 2 0 -> |x| 2. Options A and
B ignore the inner function's effect on the domain; D arises from incorrectly solving x² 2 2.
5. The function h(x) = (2x + 1)/(x 3) models the cost per unit in dollars for producing x
thousand units. Which pair correctly identifies the vertical asymptote and the horizontal
asymptote?
[ ] A. x = 3; y = 2
[ ] B. x = 3; y = 1/3
[ ] C. x = 2; y = 3
[ ] D. x = 1/2; y = 2
CORRECT: A. x = 3; y = 2
The vertical asymptote occurs where the denominator is zero: x = 3. Since the numerator and denominator
have equal degree, the horizontal asymptote is the ratio of leading coefficients: y = 2/1 = 2. Options B-D
misidentify zeros or coefficient ratios.
6. A company's revenue model is R(t) = 500e^{0.04t}, where t is years since 2020. By what
factor does revenue increase from 2020 to 2030?
[ ] A. e^{0.4}
[ ] B. e^{0.04}
[ ] C. 10e^{0.04}
[ ] D. e^{0.4} 1
CORRECT: A. e^{0.4}
The ratio R(10)/R(0) = e^{0.04(10)}/e^{0} = e^{0.4}. The factor is e^{0.4} 1.49. Options B uses one year; C
incorrectly scales by 10; D gives the increase, not the multiplicative factor.
7. Given f(x) = 3x 7, what is the value of f¹(f(5)) + f(f¹(2))?
[ ] A. 7
[ ] B. 10
[ ] C. 2
[ ] D. 12
HIGHP - Page 3 of 31
, CORRECT: A. 7
Since f and f¹ are inverses, f¹(f(5)) = 5 and f(f¹(2)) = 2. Their sum is 7. Options B-D result from incorrectly
applying the functions or adding constants.
8. The function g(x) = 2(x 4)² + 3 represents the height of a projectile. Which
transformation sequence maps y = x² to g(x)?
[ ] A. Shift right 4, reflect over x-axis, stretch vertically by 2, shift up 3
[ ] B. Shift left 4, reflect over y-axis, stretch vertically by 2, shift up 3
[ ] C. Shift right 4, stretch vertically by 2, shift up 3, reflect over x-axis
[ ] D. Shift left 4, reflect over x-axis, stretch vertically by 2, shift down 3
CORRECT: A. Shift right 4, reflect over x-axis, stretch vertically by 2, shift up 3
The form a(x h)² + k with a = 2, h = 4, k = 3 indicates: horizontal shift right 4, vertical stretch by |a| = 2,
reflection over x-axis due to negative a, and vertical shift up 3. Options B and D misplace the shift direction or
reflection axis; C reverses reflection and shift order in a way that changes the graph.
9. A rational function R(x) = (x² 9)/(x² 4x + 3) has a hole at which x-value, and what is the
y-coordinate of the hole?
[ ] A. x = 3; y = 6/2 = 3
[ ] B. x = 1; y = 8/2 = 4
[ ] C. x = 3; y = 3/1 = 3
[ ] D. x = 1; y = 4
CORRECT: C. x = 3; y = 3/1 = 3
Factor: numerator (x3)(x+3), denominator (x3)(x1). The common factor (x3) creates a hole at x = 3. Simplified
R(x) = (x+3)/(x1), so y = (3+3)/(31) = 6/2 = 3. Options A and B miscompute the y-value; D incorrectly
identifies the hole location.
10. The electricity cost function C(x) = 20 + 0.15x for x 1000 and C(x) = 0.30x 130 for x >
1000 is used to model monthly bills. Which statement about continuity at x = 1000 is
correct?
[ ] A. C is continuous because both pieces equal 170 at x = 1000.
[ ] B. C is discontinuous because the left limit is 170 and right limit is 170.
[ ] C. C is discontinuous because the left limit is 170 and right limit is 300.
[ ] D. C is continuous because the slopes are different.
CORRECT: A. C is continuous because both pieces equal 170 at x = 1000.
Evaluate both pieces at x = 1000: 20 + 0.15(1000) = 170 and 0.30(1000) 130 = 170. Since the left and right
limits equal the function value, C is continuous. Options B-D misstate limits or confuse slope changes with
HIGHP - Page 4 of 31
3 | Bungee Jump, Road Planning &
Electricity Pricing | Complete Solutions |
2026/2027 Updated | University of the People
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
97 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
Assignment Unit 3 of MATH 1201 College Algebra applies function concepts to real-world modeling tasks
including bungee jump height, road planning with polynomial curves, and electricity pricing with rational and
exponential functions. The exam assesses domain/range, rates of change, composition, transformations,
inverse functions, and asymptotic behavior through multi-step algebraic reasoning.
STUDY GUIDE
Recommended duration: 3 hours. Passing target: 70% (C or better).
HIGHP - Page 1 of 31
,1. A bungee jumper's height above ground is modeled by h(t) = 50 + 30cos(t/2) for t 0.
What is the exact time in the first cycle when the jumper is momentarily at the lowest
point, and what is that minimum height?
[ ] A. t = 1 s; h = 20 m
[ ] B. t = 2 s; h = 20 m
[ ] C. t = 1 s; h = 80 m
[ ] D. t = 2 s; h = 80 m
CORRECT: B. t = 2 s; h = 20 m
The cosine term reaches its minimum value of 1 when t/2 = , giving t = 2 s. Substituting yields h = 50 + 30(1)
= 20 m. Options A and C misplace the time; D gives the maximum height, not the minimum.
2. A road curve is designed so its elevation follows P(x) = 0.02x³ + 0.3x² + 1.5x + 2 for 0 x
10 (x in hundreds of meters). Which statement correctly describes the end behavior of P(x)
as x -> ?
[ ] A. P(x) -> because the quadratic term dominates.
[ ] B. P(x) -> because the cubic term dominates.
[ ] C. P(x) -> 0 because the constant term dominates.
[ ] D. P(x) oscillates without limit due to the cubic term.
CORRECT: B. P(x) -> because the cubic term dominates.
For a cubic with negative leading coefficient, as x -> the leading term 0.02x³ dominates and drives P(x) -> .
The quadratic term is lower degree and cannot control end behavior; polynomial functions do not oscillate.
3. An electricity company charges C(k) = 0.12k + 15 for 0 k 500, and C(k) = 0.25k 50 for k
> 500 (k in kWh). What is the domain of the inverse function that gives kWh as a function
of cost for the first tier?
[ ] A. 0 C 75
[ ] B. 15 C 75
[ ] C. 0 C 500
[ ] D. 15 C 500
CORRECT: B. 15 C 75
For the first tier, k [0, 500] maps to C(0) = 15 and C(500) = 75. The inverse's domain is the range of the
original function on that interval, i.e., [15, 75]. Options A and D confuse the input and output intervals; C uses
the kWh range instead of the cost range.
HIGHP - Page 2 of 31
,4. Let f(x) = (x 3) and g(x) = x² + 1. What is the domain of (f g)(x)?
[ ] A. All real numbers
[ ] B. x 3
[ ] C. x 2 or x 2
[ ] D. x 2
CORRECT: C. x 2 or x 2
Compute (f g)(x) = (x² + 1 3) = (x² 2). The radicand must be nonnegative: x² 2 0 -> |x| 2. Options A and
B ignore the inner function's effect on the domain; D arises from incorrectly solving x² 2 2.
5. The function h(x) = (2x + 1)/(x 3) models the cost per unit in dollars for producing x
thousand units. Which pair correctly identifies the vertical asymptote and the horizontal
asymptote?
[ ] A. x = 3; y = 2
[ ] B. x = 3; y = 1/3
[ ] C. x = 2; y = 3
[ ] D. x = 1/2; y = 2
CORRECT: A. x = 3; y = 2
The vertical asymptote occurs where the denominator is zero: x = 3. Since the numerator and denominator
have equal degree, the horizontal asymptote is the ratio of leading coefficients: y = 2/1 = 2. Options B-D
misidentify zeros or coefficient ratios.
6. A company's revenue model is R(t) = 500e^{0.04t}, where t is years since 2020. By what
factor does revenue increase from 2020 to 2030?
[ ] A. e^{0.4}
[ ] B. e^{0.04}
[ ] C. 10e^{0.04}
[ ] D. e^{0.4} 1
CORRECT: A. e^{0.4}
The ratio R(10)/R(0) = e^{0.04(10)}/e^{0} = e^{0.4}. The factor is e^{0.4} 1.49. Options B uses one year; C
incorrectly scales by 10; D gives the increase, not the multiplicative factor.
7. Given f(x) = 3x 7, what is the value of f¹(f(5)) + f(f¹(2))?
[ ] A. 7
[ ] B. 10
[ ] C. 2
[ ] D. 12
HIGHP - Page 3 of 31
, CORRECT: A. 7
Since f and f¹ are inverses, f¹(f(5)) = 5 and f(f¹(2)) = 2. Their sum is 7. Options B-D result from incorrectly
applying the functions or adding constants.
8. The function g(x) = 2(x 4)² + 3 represents the height of a projectile. Which
transformation sequence maps y = x² to g(x)?
[ ] A. Shift right 4, reflect over x-axis, stretch vertically by 2, shift up 3
[ ] B. Shift left 4, reflect over y-axis, stretch vertically by 2, shift up 3
[ ] C. Shift right 4, stretch vertically by 2, shift up 3, reflect over x-axis
[ ] D. Shift left 4, reflect over x-axis, stretch vertically by 2, shift down 3
CORRECT: A. Shift right 4, reflect over x-axis, stretch vertically by 2, shift up 3
The form a(x h)² + k with a = 2, h = 4, k = 3 indicates: horizontal shift right 4, vertical stretch by |a| = 2,
reflection over x-axis due to negative a, and vertical shift up 3. Options B and D misplace the shift direction or
reflection axis; C reverses reflection and shift order in a way that changes the graph.
9. A rational function R(x) = (x² 9)/(x² 4x + 3) has a hole at which x-value, and what is the
y-coordinate of the hole?
[ ] A. x = 3; y = 6/2 = 3
[ ] B. x = 1; y = 8/2 = 4
[ ] C. x = 3; y = 3/1 = 3
[ ] D. x = 1; y = 4
CORRECT: C. x = 3; y = 3/1 = 3
Factor: numerator (x3)(x+3), denominator (x3)(x1). The common factor (x3) creates a hole at x = 3. Simplified
R(x) = (x+3)/(x1), so y = (3+3)/(31) = 6/2 = 3. Options A and B miscompute the y-value; D incorrectly
identifies the hole location.
10. The electricity cost function C(x) = 20 + 0.15x for x 1000 and C(x) = 0.30x 130 for x >
1000 is used to model monthly bills. Which statement about continuity at x = 1000 is
correct?
[ ] A. C is continuous because both pieces equal 170 at x = 1000.
[ ] B. C is discontinuous because the left limit is 170 and right limit is 170.
[ ] C. C is discontinuous because the left limit is 170 and right limit is 300.
[ ] D. C is continuous because the slopes are different.
CORRECT: A. C is continuous because both pieces equal 170 at x = 1000.
Evaluate both pieces at x = 1000: 20 + 0.15(1000) = 170 and 0.30(1000) 130 = 170. Since the left and right
limits equal the function value, C is continuous. Options B-D misstate limits or confuse slope changes with
HIGHP - Page 4 of 31
