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1**.**Verify the identity**. **Show your work.

cot Î¸ âˆ™ sec Î¸ csc Î¸

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? Show your work.

What is the charge for using 45 therms in one month? Show your work.

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

**3.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.** Show your work.

**(c) Find the y-intercept.** Show your work.

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

(a).

(b).

(c).

4.Verify the identity. Show your work.

(1 + tan^{2}u)(1 – sin^{2}u) 1

**5.Verify the identity**. Show your work.

cot^{2}x + csc^{2}x 2csc^{2}x – 1

6.Verify the identity. Show your work.

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

**7.Verify the identity. **Show your work.

cos(Î± – Î²) – cos(Î± + Î²) 2 sin Î± sin Î²

8.Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.

f(x) x-4/x(x-4)

9.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? Show your work.

10.Find the specified vector or scalar. Show your work.

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

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

cot(-5Ï€/4)

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

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

Give your answers in exact form. Show your work.

13.Use the compound interest formulas A Pe^{rt} and A P(1+r/n)^nt 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? Show your work.

14.Find functions f and g so that h(x) (f âˆ˜ g)(x).

h(x) (6x – 14)^{8}

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

h(x) 2 | x | + 2

16.Find the reference angle for the given angle. Show your work.

-404Â°

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