Short Answer: Type your answer below each question. Show your work.

1

Verify the identity.

cot θ ∙ sec θ = csc θ

2

A gas company has the following rate schedule for natural gas usage in single-family residences:

Monthly service charge $8.80

Per therm service charge

1st 25 therms $0.6686/therm

Over 25 therms $0.85870/therm

What is the charge for using 25 therms in one month?

What is the charge for using 45 therms in one month?

Construct a function that gives the monthly charge C for x therms of gas.

3

The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is

W(t) =

where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)

4

Complete the following:

(a) Use the Leading Coefficient Test to determine the graph’s end behavior.

(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept.

(c) Find the y-intercept.

f(x) = x^{2}(x + 2)

(a).

(b).

(c).

5

For the data set shown by the table,

a. Create a scatter plot for the data. (You do not need to submit the scatter plot)

b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data.

Number of Homes Built in a Town by Year

6

Verify the identity.

(1 + tan^{2}u)(1 – sin^{2}u) = 1

7

Verify the identity.

cot^{2}x + csc^{2}x = 2csc^{2}x – 1

8

Verify the identity.

1 + sec^{2}xsin^{2}x = sec^{2}x

9

Verify the identity.

cos(α – β) – cos(α + β) = 2 sin α sin β

10

The following data represents the normal monthly precipitation for a certain city.

Draw a scatter diagram of the data for one period. (You do not need to submit the scatter diagram). Find the sinusoidal function of the form that fits the data.

Multiple Choice: Type your answer choice in the blank next to each question.

_____11.

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

Does the graph represent a function?

A. Yes

B. No

_____12.

Find the vertical asymptotes, if any, of the graph of the rational function.

f(x) =

A. x = 0 and x = 4

B. x = 0

C. x = 4

D. no vertical asymptote

_____13.

The formula A = 118e^{0.024t} models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand?

A. 2008

B. 2005

C. 2006

D. 2007

_____14.

Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find .

A.

B. 8

C. 2

D. 5

_____15.

Find the exact value of the trigonometric function. Do not use a calculator.

A. -1

B.

C. 1

D.

_____16.

Find the x-intercepts (if any) for the graph of the quadratic function.

6x^{2} + 12x + 5 = 0

Give your answers in exact form.

A.

B.

C.

D.

_____17.

Use the compound interest formulas A = Pe^{rt} and A = Pto solve.

Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?

A. $11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.

B. Both investment plans yield the same return.

C. $11,000 invested at 6.3% compounded semiannually over 10 years yields the greater return.

_____18.

Find functions f and g so that h(x) = (f ∘ g)(x).

h(x) = (6x – 14)^{8}

A. f(x) = 6x – 14, g(x) = x^{8}

B. f(x) = 6x^{8} – 14, g(x) = -14

C. f(x) = x^{8}, g(x) = 6x – 14

D. f(x) = (6x)^{8}, g(x) = -14

_____19.

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to graph the given function.

h(x) = 2 | x | + 2

A.

B.

C.

D.

_____20.

Find the reference angle for the given angle.

-404°

A. 44°

B. 46°

C. 134°

D. 136°

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