a. Sketch the graph of $f(x)=x^{2}-\frac{3}{x}$, for $-4 \leq x \leq 4$. b. Write down the equation of the vertical asymptote of f(x). c. On the same diagram draw the graph of $g(x)=-3(2)^{x}+9$, for $-4 \leq x \leq 4$. d. Write down the equation of the horizontal asymptote of g(x). e. Find the coordinates of the points of intersection of f(x) and g(x).

Use the graphical method to find all solutions of the system of equations, correct to two decimal places.

$$\left\{\begin{array}{l}x^4+16 y^4=32 \\ x^2+2 x+y=0\end{array}\right.$$

Fill in the blank or circle the letter of the best answer.

Hodos and iter both mean _____________________.

Write the function whose graph is the graph of $y=\sqrt{x}$, but is transformed accordingly, and state the domain of the resulting function.

Shifted down four units

For each pair of terms, explain the differences in their meanings.

a. weather

climate

b. atmosphere

ozone

c. greenhouse effect global warming

d. troposphere stratosphere

Use the graphical method to find all solutions of the system of equations, rounded to two decimal places.

$$\left\{\begin{array}{l}x^4+16 y^4=32 \\ x^2+2 x+y=0\end{array}\right.$$

Which pairs of triangles are congruent by SAS? By SSS?

Given the system of equations

$$\begin{array}{l}{0.77 x_{1}+x_{2}=14.25} \\ {1.2 x_{1}+1.7 x_{2}=20}\end{array}$$

(a) Solve graphically and check your results by substituting them back into the equations. (b) On the basis of the graphical solution, what do you expect regarding the condition of the system? (c) Compute the determinant.

Use the graphical method to find all solutions of the system of equations, rounded to two decimal places.

$$\left\{\begin{array}{l}x^2-y^2=3 \\ y=x^2-2 x-8\end{array}\right.$$

Write down the first five terms of each sequence. $\left\{b_{n}\right\}=\left\{(-1)^{n-1} \frac{n}{n+1}\right\}$

In this exercise, you will investigate the graphical effect of completing the square. a. Graph each pair of functions in the same coordinate plane.

$$\left. \begin{array} { l l } { y = x ^ { 2 } + 2 x } & { y = x ^ { 2 } - 6 x } \\ { y = ( x + 1 ) ^ { 2 } } & { y = ( x - 3 ) ^ { 2 } } \end{array} \right.$$

b. Compare the graphs of

$$y = x ^ { 2 } + b x\ and\ y = \left( x + \frac { b } { 2 } \right) ^ { 2 }.$$

Describe what happens to the graph of

$$y = x ^ { 2 } + b x$$

when you complete the square.

Think of the set $\Omega$={H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T} as the outcome space for three tosses of a coin. For example, the subset $\{H H H, T T T\}$ corresponds to the event that all three tosses land the same way. Give similar verbal descriptions for the events described by each of the following subsets of $\Omega$.

a) $\{H H H, H H T, H T H, H T T\}$

b) $\{H T H, H T T, T T T, T T H\}$

c) $\{\mathrm{HTT}, \mathrm{HTH}, \mathrm{HHT}, \mathrm{HHH}\}$

d) $\{\mathrm{HHH}, \mathrm{HHT}, \mathrm{HT} \cdot \mathrm{H}, \mathrm{THH}\}$

e) $\{$ THT $, H T T, T T H\}$

f) $\{$ HHT,HHH,TTH,TTT $\}$

Solve the equation given below and give your best answer.

$|x+3|=|2 x+1|$

Solve the exercise given below. Write the correct answer.

$$c: \frac{2}{c}-\frac{5}{c^2+c}=\frac{5}{c+1}$$