1
MATH 115 Quiz2_Fall2018
NAME: ______________________________
By signing my name above, I certify that I have completed this assignment individually,
working independently and not consulting anyone except the instructor.
Instructions for QUIZ 2:
The quiz is worth 100 points. There are 12 problems, some with several parts; point totals are
indicated by each part.
QUIZ 2 is based on Chapter 0 (Sections 0.7 and 0.10) of the “Precalculus Prerequisites a.k.a.
Chapter 0”; and Chapter 2 (Sections 2.1, through 2.5) and Chapter 3 (Section 3.1) of the
“College Algebra, 3 rd
Corrected Edition” text. It is open book and open notes. This means that
you may refer to your textbook, notes, and online classroom materials, but you must work
independently and may not consult anyone (and confirm this with your submission). YOU
MAY USE YOUR GRAPHING CALCULATOR (TI-83/84 or EQUIVALENT, nothing more
sophisticated) TO ASSIST IN GRAPHING OR ANY NUMERICAL CALCULATIONS).
You must show your work. Answers without any work may earn little, if any, credit. You
may type or write your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is acceptable also.
When you have completed the quiz, upload your solutions file to the Quiz 2 assignment in the
Assignment folder. DUE DATE is NLT 11:59pm EDT, Sunday, September 9.
If you have any questions, please contact me by e-mail.
——————————————————————-
1. (6 pts). Determine the equation (IN SLOPE-INTERCEPT FORM) for the line passing through the
point (30, –8) and parallel to the line x + 5y = 20
Equation (in Slope-Intercept Form): _______________________________
2
2. (6 pts). Determine the equation (IN SLOPE-INTERCEPT FORM) for the line passing through the point (7, 5) which is perpendicular to the line 2x + y = – 15
Equation (in Slope-Intercept Form): _______________________________
3. (6 pts). Determine a correct equation for the line whose graph is sketched below.
Equation: _______________________________
3
4. (18 pts). Consider the function f(x) = 3|x – 5| + 5.
Answer the following questions and then sketch a graph of the function:
(a). Find the x-intercept(s) of the function: ________________.
(b). Find the y-intercept of the function: __________________.
(c). Find the domain of the function: ______________________.
(d). Find the range of the function: ________________________.
(e). List the interval(s) where the function is increasing: __________________________.
(f). List the interval(s) where the function is decreasing: ____________________________.
(g). Determine the relative and absolute minimum (if any exist): _________________________________.
(h). Determine the relative and absolute maximum (if any exist): _________________________________.
4
5. (8 pts). Find all real solutions to the following equation:
5 – t = 2(t + 1) 2
Answers: t = _________________________________
6. (8 pts). Find all real solutions to the following equation:
x 4 + 5x
2 – 1 = 0 (Hint: Make a substitution which would turn this into a quadratic equation)
Answers: x = _________________________________
5
7. (8 pts). Find all real solutions to the following equation:
𝒙
𝟗𝒙+𝟒 = 3
Answers: x = _________________________________
8. (8 pts). Find all real solutions to the following equation:
𝟒𝐱 − 𝐱𝟑
𝐱𝟐 − 𝟗 = 𝟒𝐱
Answers: x = _________________________________
6
9. (8 pts). For the complex numbers z = 3 – 5i and w = 2 + 5i, find the following (simplify and
write each answer in the form a + bi):
(a). zw
Answer: zw = _________________________________
(b). 𝐳
𝐰
Answer: z/w = _________________________________
7
10. (12 pts). For the following quadratic function, answer the following questions and then
sketch a graph on the coordinate axes below:
f(x) = 2x 2 – 5x – 1
(a). Domain of f(x) : ________________ (b). Range of f(x):__________________
(c). Coordinates of the vertex: _____________; Circle One: Relative minimum or maximum
(d). Coordinates of the x-intercept(s): ___________
(e). Coordinates of the y-intercept: __________
(f). Sketch the graph on the coordinate axes below.
8
11. (6 pts). Solve the following inequality. WRITE YOUR ANSWER USING INTERVAL NOTATION.
x + | 2x – 3 | < 3
Answer (in interval notation): ________________________________
12. (6 pts). Solve the following inequality. WRITE YOUR ANSWER USING INTERVAL NOTATION.
x 2 + 4x ≥ 12
Answer (in interval notation): ________________________________
