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Verify the identity.


cot θ ∙ sec θ = csc θ









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.













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.)






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) = x2(x + 2)





















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






Verify the identity.

(1 + tan2u)(1 – sin2u) = 1





Verify the identity.

cot2x + csc2x = 2csc2x – 1






Verify the identity.

1 + sec2xsin2x = sec2x





Verify the identity.

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








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.



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




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












The formula A = 118e0.024t 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



Find the specified vector or scalar.

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



B. 8


C. 2


D. 5



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


A. -1




C. 1





















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

6x2 + 12x + 5 = 0

Give your answers in exact form.













Use the compound interest formulas A = Pert and A = P to 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.



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

h(x) = (6x – 14)8

A. f(x) = 6x – 14, g(x) = x8


B. f(x) = 6x8 – 14, g(x) = -14


C. f(x) = x8, g(x) = 6x – 14


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




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










Find the reference angle for the given angle.


A. 44°


B. 46°


C. 134°


D. 136°


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