Find an appropriate graphing software viewing window for the given function and use it to display its graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function. $y=x+\frac{1}{10} \sin 30 x$

Graph y = sin x and $y=\lfloor\sin x\rfloor$ together. What are the domain and range of $\lfloor\sin x\rfloor ?$

Write an equation for each line described.

Passes through $(4,10)$ and is perpendicular to the line $6 x-3 y=5$

Find the domain. $y=\ln (x-3)+1$

Tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $y=\sqrt{x}$ Left 0.81

Solve the inequalities, expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line.

$$|2 s| \geqslant 4$$

Find the range.

$$y=\ln (x-3)+1$$

How does $f(x)=\log _x(2)$ compare with $g(x)=\log _2(x)$ ? Here is one way to find out. Use the equation $\log _a b=(\ln b) /(\ln a)$ to express $f(x)$ and $g(x)$ in terms of natural logarithms. Graph $f$ and $g$ together. Comment on the behavior of $f$ in relation to the signs and values of $g$.

Find the domain:

$$y=-1+\sqrt[3]{2-x}$$

Graph y = tan x and y = cot x together for $-7 \leq x \leq 7.$ Comment on the behavior of cot x in relation to the signs and values of tan x.

Solve the inequalities, expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line.

$$|\frac{2}{x}-4|<3$$

Use graphs to find approximate solutions. $3-2^{-x}=0$

How does $f(x)=\log _x(2)$ compare with $g(x)=\log _2(x)$ ? Here is one way to find out. Use the equation $\log _a b=(\ln b) /(\ln a)$ to express $f(x)$ and $g(x)$ in terms of natural logarithms.

Say whether the function is even, odd, or neither. Give reasons for your answer.

$h(t)=\left|t^3\right|$