ALG 213 | September 13, 2025
James Wright
Prof. Dr.Mary Roberts
ALG 213
Mountain Riverside University
Advanced Algebra Problems
With Solutions
Problem 1: Analyze and sketch the cubic polynomial f(x) = -1x³ - 2x² - 2x + 2 Find: a) End
behavior, b) y-intercept, c) Critical points (approximate)
Solution:
Given: f(x) = -1x³ - 2x² - 2x + 2
a) End behavior:
Leading coefficient is -1 (negative)
As x → ∞: f(x) → -∞
As x → -∞: f(x) → +∞
b) y-intercept: f(0) = 2
Point: (0, 2)
c) Critical points found by solving f'(x) = 0:
f'(x) = -3x² - 4x - 2
Using quadratic formula on f'(x) = 0...
(Critical points require numerical methods for exact values)
Note: At first I tried a different method, but then realized
Problem 2: A plumber charges 69.93 for a service call plus 3.29 per hour of work. If the total
cost is $116.34, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
116.34 = 69.93 + 3.29x
Solving for x:
116.34 - 69.93 = 3.29x
46.41 = 3.29x
x = 46.41 ÷ 3.29
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:40:44 GMT -05:00
https://www.coursehero.com/file/251540619/MTH-285I-Algebra-Solutions-2700docx/
, ALG 213 | September 13, 2025
x = 14.1 hours
Reasoning:
Check: 69.93 + 3.29(14.1) = 69.93 + 46.39 = 116.32 ✓
(Reminder: Don't forget the units in the final answer)
Problem 3: A plumber charges 65.09 for a service call plus 4.39 per hour of work. If the total
cost is $316.07, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
316.07 = 65.09 + 4.39x
Solving for x:
316.07 - 65.09 = 4.39x
250.98 = 4.39x
x = 250.98 ÷ 4.39
x = 57.2 hours
Alternative approach:
Check: 65.09 + 4.39(57.2) = 65.09 + 251.11 = 316.20 ✓
Problem 4: A rental car costs 45.78 per day plus 0.91 per mile. If the total cost is $360.44,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
360.44 = 45.78 + 0.91x
Solving for x:
360.44 - 45.78 = 0.91x
314.66 = 0.91x
x = 314.66 ÷ 0.91
x = 345.8 miles
Step-by-step verification:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:40:44 GMT -05:00
https://www.coursehero.com/file/251540619/MTH-285I-Algebra-Solutions-2700docx/
James Wright
Prof. Dr.Mary Roberts
ALG 213
Mountain Riverside University
Advanced Algebra Problems
With Solutions
Problem 1: Analyze and sketch the cubic polynomial f(x) = -1x³ - 2x² - 2x + 2 Find: a) End
behavior, b) y-intercept, c) Critical points (approximate)
Solution:
Given: f(x) = -1x³ - 2x² - 2x + 2
a) End behavior:
Leading coefficient is -1 (negative)
As x → ∞: f(x) → -∞
As x → -∞: f(x) → +∞
b) y-intercept: f(0) = 2
Point: (0, 2)
c) Critical points found by solving f'(x) = 0:
f'(x) = -3x² - 4x - 2
Using quadratic formula on f'(x) = 0...
(Critical points require numerical methods for exact values)
Note: At first I tried a different method, but then realized
Problem 2: A plumber charges 69.93 for a service call plus 3.29 per hour of work. If the total
cost is $116.34, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
116.34 = 69.93 + 3.29x
Solving for x:
116.34 - 69.93 = 3.29x
46.41 = 3.29x
x = 46.41 ÷ 3.29
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:40:44 GMT -05:00
https://www.coursehero.com/file/251540619/MTH-285I-Algebra-Solutions-2700docx/
, ALG 213 | September 13, 2025
x = 14.1 hours
Reasoning:
Check: 69.93 + 3.29(14.1) = 69.93 + 46.39 = 116.32 ✓
(Reminder: Don't forget the units in the final answer)
Problem 3: A plumber charges 65.09 for a service call plus 4.39 per hour of work. If the total
cost is $316.07, find the number of hours used.
Solution:
Let x = number of hours
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
316.07 = 65.09 + 4.39x
Solving for x:
316.07 - 65.09 = 4.39x
250.98 = 4.39x
x = 250.98 ÷ 4.39
x = 57.2 hours
Alternative approach:
Check: 65.09 + 4.39(57.2) = 65.09 + 251.11 = 316.20 ✓
Problem 4: A rental car costs 45.78 per day plus 0.91 per mile. If the total cost is $360.44,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
360.44 = 45.78 + 0.91x
Solving for x:
360.44 - 45.78 = 0.91x
314.66 = 0.91x
x = 314.66 ÷ 0.91
x = 345.8 miles
Step-by-step verification:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:40:44 GMT -05:00
https://www.coursehero.com/file/251540619/MTH-285I-Algebra-Solutions-2700docx/
