Math 180Name______
Fall Semester 2006
Final Exam
WORK MUST BE SHOWN TO RECEIVE CREDIT. CIRCLE YOUR ANSWERS.
1. Find for
2) Solve the equation.
3. Find, simplify and state the domain of for the functions
, and
4.Consider the rational function :
(a)State the domain of the function.
(b)Write the equation of any vertical asymptotes.
(c)Write the equation of any horizontal asymptotes.
(d)Write the coordinates of any holes.
(e)List any x-intercepts.
(f)List any y-intercepts.
(g)Graph and label any asymptotes, intercepts, and holes.
(h)State the range of this function.
(i)Complete this statement:As , .
5) Establish the identity.
6. Four functions are graphed below. Classify each of them as exponential, logarithmic, polynomial,
rational, sinusoidal or none of the above.
7. Given the equation do EACH of parts (a), (b), and (c).
(a) Solve the equation algebraically. (You can use degrees, but write final answers in radians). Circle all answers.
(b)Graph the relationship described in the given equation on the specified domain. On the graph, mark and label the location of each solution, including its coordinates. Use radian mode, and round answers to the nearest four decimal places. Make sure the answers match your solutions to part (a)
Use proper scales on both axes.
8. There was a flu epidemic at StateUniversity. The graph below shows the total number of cases of flu, as reported by the StudentHealthCenter during the epidemic. Use the graph to answer the questions below, based on the StudentHealthCenter data.
(a)About how many students had the flu when the outbreak began? a) ______
(b)About how many students had the flu on the sixth day of the flu outbreak? b)______
(c) How long did it take for 1300 students to come down with the flu,
once the outbreak began? c)______
(d)During which five-day span were there more new cases of the flu between
day 5 and day 10 or between day 15 and day 20? d)______
Justify your answer, using complete sentence(s).
(e)Estimate the average rate of change in the flu cases between day 5 and day 10.
e)______
(f) On which of these days are the flu cases increasing the fastest?
Day 2, day 4, day 8, day 16 or day 32? f)______
(g)What does the graph suggest is the total number of cases of flu during this epidemic? g)______
9. For the following function:
(a) Find the zeros and identify them as rational, irrational, or non-real complex.
The zeros are: (remember to classify them as rational, irrational, or complex)
......
(b) Factor the polynomial completely over the complex numbers.
10) Use the diagram to answer the following questions. Write your answers exactly.
a)
b)
c)
11) The figure below shows the graphs of y = sin x and
y = cos x starting at x = 0.
- Which is y = cos x?
- Which is?
- Find values for a, b and c.
Do not use decimal approximations.
a = ______b = ______c = ______
d. Use the graph to solve sin x ≤ cos xfor x in the interval [0, c]
Do not use decimal approximations.
12. Use the functions f and g to evaluate the following.
(a)(f + g ) (1)
(b)(f g ) (3)
(c)(d)(f g) (1)
(e)(f)
13. The half-life of silicon-32 is 710 years. Construct an exponential model for the amount of silicon-32 remaining after t years. Use . Approximate k to 5 decimal places.
The exponential model is......
(b) If 40 grams of silicon-32 are present now, use the exact value of k to find how much will be present after 200 years.
14) Given . Find
a) Domain:
b) Range:
c) Asymptote(s):
d) x-intercept(s): (round to nearest hundredth)
e) y-intercept:
f) Graph. Label all intercepts and asymptotes.
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