Recall the quotient identity $\tan x=\frac{\sin x}{\cos x}$. Use the graphs of y = sin x and y = cos x in conjunction with the quotient identity to explain the shape of the graph of y = tan x.

You want to redecorate your bedroom and need to measure the room for new carpeting, paint, and a border on the walls. You realize that you have only a meter stick. You measure the room, but you need to know the dimensions in feet to purchase the materials. You record these measurements: -The length of the room is 5 meters. -The width of the room is 4 meters. - The height of the room is 2.5 meters. Use a double number line to determine the measurement of each dimension in feet. a. length b. width c. height

Find $f^{\prime}(x)$ and simplify. $f(x)=\frac{3 x}{2 x+1}$

Calculate the percentage change in the CPI between the two years shown. Round your answers to the nearest tenth of a percent.

$$\begin{matrix} \text{Year} & \text{CPI}\\ \text{2000} & \text{168.8}\\ \text{2005} & \text{190.7}\\ \end{matrix}$$

Percentage change in CPI _____________

Create a number line from -6 to -5. Your goal is to plot and label a rational number closer to -5 than your partner. Partner 1: Plot a rational number, A, between -6 and -5 that is close to -5. Partner 2: Plot a rational number, B, between A and -5. Repeat at least 2 more times.

Using the CRC Handbook of Chemistry and Physics (available in most libraries) or an online reference, find the following for the element tellurium: (a) Melting point (b) Color (c) Density (d) Uses

Let $f(x)=(x-3)^{2}$ and g(x) = x + 4. Determine an algebraic and a graphical model for each combined function. Give the domain and range in each case. a) y = f(x) + g(x) b) y = f(x) - g(x) c) y = f(g(x)) d) $y=g^{-1}(g(x))$

Graph each function. a) y = -log (x - 4) b) y = log (-x) - 3

Prove. a) $\cos \left(\sin ^{-1} x\right)=\sqrt{1-x^{2}}$ b) $\cos ^{-1} a+\cos ^{-1} b =\cos ^{-1}\left(a b-\sqrt {1-a^{2}} \sqrt {1-b^{2}}\right)$, for a, b > = 0

At a point on a conducting surface, $\mathbf{E}=30 \mathbf{a}_{x}-40 \mathbf{a}_{y}+20 \mathbf{a}_{z} \mathrm{mV} / \mathrm{m}$. Calculate the surface charge density at that point.

Which are not examples of average rates of change? Explain why. a) The average height of the players on the basketball team is 2.1 m. b) The temperature of water in the pool decreased by $5^{\circ} \mathrm{C}$ over 3 days. c) The snowboarder raced across the finish line at 60 km/h. d) The class average on the last math test was 75%. e) The value of the Canadian dollar increased from $0.75 U.S. to$1.01 U.S. in 8 months. f) Approximately 30 cm of snow fell over a 5-h period.

These functions are each defined for the given domain. Find their ranges. (a) $f(x)=2 x \text { for } 0 \leqslant x \leqslant 8$ (b) $f(x)=3-2 x \text { for }-2 \leqslant x \leqslant 2$ (c) $f(x)=x^{2} \text { for }-1 \leqslant x \leqslant 4$ (d) $f(x)=x^{2} \text { for }-5 \leqslant x \leqslant-2$

Select one trigonometric identity from each of previous questions. Use graphing technology to verify the identities.

In 2015, a retired person in the United States who received maximum social security benefits got $2699 per month, which represented a 1.7% cost of living adjustment (COLA) over 2014. (a) Determine the monthly benefit in 2018 if the COLA adjustments are 1.5%, 2.1%, and 2.7%, respectively, for the next 3 years. (b) Assuming the average annual inflation is 2.0% per year, determine if the monthly benefits in 2018 have more or less purchasing power in current-value terms assuming the 3 years of COLA adjustments above.