Math 115 MidtermSpring, 20151
Math 115PreCalculusName ______
Midterm: Spring, 2015
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
There are 15 problems.
When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. You must submit a single file in commonly used formats for example word processing or PDF. Do not submit JPEG or any other image files.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I have completed this midterm examination myself; working independently and not consulting anyone except the instructor. I have neither given nor received help on this midterm examination.
Name ______Date_041115______
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number / Solution1 / For the pair of functions find the indicated information
F(x)=x2-9, g(x)=2x+3
a. Find the domain of f.
Step1. Make 0 the denominator
X=3 that will make X2-9=0
32-9=0
The domain of f will be a set of real numbers excluding 9. With the interval notation the domain of f is
Answers
Domain of f
(-∞,3)U(3,∞)
b. Find the domain of g.
Step2. Make 0 the denominator
2x+3=0
-3 -3
2x=-3 Divide 2 into 3
Answers
X=-3/2
Domain of G
(-∞,-3/2)U(-3/2, ∞)
c. Find g ∘ f.
d. Find the domain of g ∘ f.
2 / Description of the transformation:
Graph:
Work:
3 / Answer: (Write your answers in the form of a+bi)
Work:
Answer:
4 / Exact solutions:
Work: (completing square)
5 / a. Vertex:
b. Axis of symmetry:
c. x-intercepts (if any-write in coordinate form):
d. y-intercept (if any - write in coordinate form):
e. Range (write in interval notation):
f. Graph:
6 / Answer:
Work:
7 / Answer:
Work:
8 / Answer:
Work:
9 / The amount of money in the account at the end of 5 years:
Work:
10 / =
Work:
11 / =
Work:
12 / a. The degree:
b. The leading term:
c.Find the zero(s). State each zero and it’s multiplicity. For each zero, state whether the graph crosses the x-axis or touches the x-axis and turns around.
Zero / Multiplicity / Crosses or touches and turns
d. Domain (State in interval notation):
13 / a) Sketch or state the end behavior:
b)
Zero / Multiplicity / Crosses or touches and turns
c) y-intercept(State as a coordinate point):
d) Maximum number of possible turning points:
e) Sketch the graph of the polynomial function.
14 / a. Domain (State in interval notation):
b. Vertical asymptote(s) (if any):
c. Horizontal asymptote (if any):
d. x-intercept(s) (if any - write as coordinate points):
e. y-intercept (if any - write as coordinate point):
f. Range (State in interval notation):
e. Graph:
15 / a. Show that the given function is one-to-one:
b. Find a formula for the inverse function:
c. Graph the function as a solid curve and its inverse as a dashed curve:
Don’t forget to sign the honor statement.
I have completed this midterm examination myself; working independently and not consulting anyone except the instructor. I have neither given nor received help on this midterm examination.
Name ______Date______