Piecewise linear functions Graph the following functions.
$f\left(x\right)=\{\begin{array}{c}3x-1\frac{}{},\text{ if }x\le 0\\ -2x-1,\text{ if }x>0\end{array}$

Taxicab fees A taxicab ride costs \$3.50 plus \$2.50 per mile for the first 5 miles, with the rate dropping to \$1.50 per mile after the fifth mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the piecewise linear function c(m) that represents the cost of taking a taxi from the airport to a hotel m miles away.

Find the inverse function (on the given interval, if specified) and graph both $f$ and $f^{-1}$ on the same set of axes. Check your work by looking for the required symmetry in the graphs.

$f\(\left\)(x\(\right\))=x^2+4$, for $x\(\geq{0}\)$

Graphing functions Sketch a graph of each function.

ƒ(x) = { 2x if x ≤ 1 , 3-x if x > 1

{Use of Tech} Launching a rocket A small rocket is launched vertically upward from the edge of a cliff $80$ ft above the ground at a speed of $96$ ft/s. Its height (in feet) above the ground is given by $h\(\left\)(t\(\right\))=-16t^2+96t+80$, where $t$ represents time measured in seconds.

a. Assuming the rocket is launched at $t=0$, what is an appropriate domain for $h$?

Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of $10$ m² is filled to a depth of $25$ m with water. At $t=0$ s, a drain in the bottom of the tank with an area of $1$ m²  is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time $t\(\geq{0}\)$ is $d\(\left\)(t\(\right\))=\(\left\)(5-0.22t\(\right\))^2$.

a. Check that $d\(\left\)(0\(\right\))=25$, as specified.

Graphing equations Graph the following equations. 

c. x² + 2x + y² + 4y + 1 = 0