Evaluate $f\left(x\right)$ at the given points.
$$f\left(x\right)=\begin{cases} {x+9}&{\begin{matrix} {\text{if}}&{x<4}\\ \end{matrix}}\\ {x^{2}+2x-2}&{\begin{matrix} {\text{if}}&{10\leq x\leq100}\\ \end{matrix}}\\ {\frac{x}{200}}&{\begin{matrix} {\text{if}}&{200<x}\\ \end{matrix}}\\ \end{cases}$$

Determine the intervals of increase, intervals of decrease, local maxima, and local minima of the graphed function below.

Given $f\left(x\right)=-4x$ and $g\left(x\right)=x^{2}$, evaluate $\left(f\circ g\right)\left(3\right)$ and $\left(g\circ f\right)\left(3\right)$. 

Given $f\left(x\right)=x^{2n}-4x^{n}-5$, and $g\left(x\right)={\sqrt[n]{{\sqrt[]{x+9}}+2}}$, where $n >0$ and $\,x\geq{\sqrt[n]{2}}$. Determine whether $g=f^{-1}$.

Pizza is being ordered for a party. The host will eat $5$ slices, but each guest will only eat $3$ slices. Write a formula for the number of slices eaten, $S$, as a function of the number of guests, $g$. Assuming that one pizza is eight slices, how many pizzas should the host order if he plans to invite $10$ guests?

Only whole pizzas may be ordered.

A speed trap records the speed of a car every half second. Below is a recording of one of the cars that passes through the speed trap.

Use the table to write the linear equation for the car's speed $K(s)$ in the speed trap. Assuming that the car is in the speed trap for $5$ seconds, how fast will it be coming out of it?

Two cars start at an intersection. They then drive away in perpendicular directions. The Car 1 is going $48$ miles per hour north, while the Car 2 is going $55$ miles per hour east. When will the two cars be $10$ miles apart from each other?

Find the intercepts of the parabola whose function is $f\left(x\right)=x^{2}-2x-48$.

Determine the quadratic function that is represented by the points given in the table.

Find the domain and the range of the parabola $$y=3x^{2}+4x+1$$

Use the Rational Zero Theorem to find any rational zeros of $f(x)=5x^4 +14x^3 + 12x^2 + 7x - 2$.

Give all your answers in an increasing order.

Determine the inverse of  $$y=\Va ^{x\VPlusb }\VPlusc $$

Solve $\log_{}\left(x^{2}-x\right)=\log_{}\left(6\right)$

A parachuter is preparing for a jump down a canyon. He estimates that the distance between his starting point and his landing point is $2.31\ukm$ away. He also estimates that the angle of descent between the two points is $9^{\circ}$. How high is the parachuter from his landing point? Round your answer to three decimal places.

Given the function $f\left(x\right)=\VA \tan\left(\VB x\VMinusC \right)$, determine:

• The stretching factor
• The phase shift
• The period
• The vertical asymptotes

Evaluate $$\sin\left(\sin^{-1}\left(\frac{2}{3}\right)+ \cos^{-1}\left(\frac{5}{6}\right)\right)$$

Write  $$\sec\left(\frac{2\pi}{11}\right)$$  in terms of its cofunction.

Parametrize the curve given $x^{3}+1=y^{4}-y^{2}$ by setting  $y(t)=t$.

Write this set of parametric equations as a Cartesian equation.
$\begin{cases} {x\left(t\right)=}&{t^{4}}\\ {y\left(t\right)=}&{t^{12}}\\ \end{cases}$

Mila purchased a small refrigerator for her kitchen. The diagonal of the front of the refrigerator measures $29$ inches. The front also has an area of $420$ square inches. What are the length and width of the refrigerator?

Let $x$ be the width and $y$ be the length.

Given the three matrices below.

$A=\begin{bmatrix} {3}&{-4}\\ {1}&{-2}\\ \end{bmatrix},\,B=\begin{bmatrix} {0}&{2}\\ {-3}&{1}\\ \end{bmatrix},\,C=\begin{bmatrix} {-5}&{3}\\ {2}&{-4}\\ \end{bmatrix}$

Find $A+B+C$, $A+B-C$, and $A-B+C$.

Find the determinant for the following:

$$\begin{bmatrix} {\Va }&{\Vb }&{\Vc }\\ {\Vd }&{\Ve }&{\Vf }\\ {\Vg }&{\Vh }&{\Vi }\\ \end{bmatrix}$$

Identify the conic section produced by the equation $x^2-4y^2+4x+24y-36=0$. Change the equation into standard form.

Evaluate $$\lim_{x\to 9}\frac{x^{2}-81}{{\sqrt[]{x}}-3}$$

Given the piecewise function below,

$f\left(x\right)=\begin{cases} {\frac{x^{2}-5x+4}{x-1}}&{x<6}\\ {9-x}&{x\geq6}\\ \end{cases}$

Characterize all discontinuity points.