Use transformations of the graph of $y = \frac { 1 } { x }$ or $y = \frac { 1 } { x ^ { 2 } }$ to graph each rational function f(x). $f ( x ) = \frac { 3 x ^ { 2 } + 18 x + 28 } { x ^ { 2 } + 6 x + 9 }$

An element has two naturally occurring isotopes. The isotope has a mass of 62.9396 amu and a relative abundance of 69.17 %, and isotope 2 has a mass of 64.9278 amu.

Find the atomic mass of this element.

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=-\frac{1}{2} x^2+4 x-2$$

Find the sum. 9.6 + 5.49

An initial amplitude k, damping constant c, and frequency f or period p are given. (Recall that frequency and period are related by the equation f=1 / p.)

(a) Find a function that models the damped harmonic motion. Use a function of the form $y=k e^{-c t} \cos \omega t$ in Exercises given below.

(b) Graph the function.

$$k=2, \quad c=1.5, \quad f=3$$

Write T (true) or F (false) for the following statement.

Semicolons and colons are always placed outside closing quotation marks.

Evaluate the expression. -6 + 3 - (-1) + 11

How are computers used in pavement management?

Respond to the following questions using the previous story:

(a) In "En el Jardin De Los Espejos Quebrados ...," what kinds of marks disfigure Caliban's body?

(b) Analyze What do these marks suggest about Caliban's supposed ugliness?

Use proofreading marks to correct any capitalization errors in the following sentence. Indicate the total number of changes at the right.

Regulations of the sarbanes-oxley act of 2002 resulted in costly expenses for our Company. _________

Graph each function on the interval $[-2 \pi, 2 \pi]$. For the trigonometric functions, explain how the graphs are transformations of $y=\sin x$ or $y=\cos x$.

$$H(x)=-\frac{1}{3} \sin x$$

By graphing the function f(x) = (tan 4x)/x and zooming in toward the point where the graph crosses the y-axis, estimate the value of lim x→0 f(x).

Find the derivatives of the given functions.

$$y =\sqrt{x^2+1}-\ln \frac{1+\sqrt{x^2+1}}{x}$$

Using what you have learned about transformations of the graph $y=\frac{1}{x}$, can you find the equations of the asymptotes of the function $f(x)=\frac{p}{c x+d}+q$, and hence state the domain and range?