Find the distance between the points $P(-1,3)$ and Q(2, 5).

Find the midpoint of the line segment joining $P(2,-5)$ and $Q(-8,-3).$

Find the x- and y-intercepts of the graph of the equation $y=x^2-2x-8$ and sketch the graph.

$x+3y-6=0$

$x=2y-6$

Find an equation in standard form of the circle with center $(2,-3)$ and radius 4.

Find the center and radius of the circle with equation

The line has slope 3 and passes through $(1,-2).$

The line is parallel to $2x+3y=5$ and passes through (1, 3).

$f(x)={\displaystyle \frac{1}{2x+3}}$

$p(x)={\displaystyle \frac{1}{\sqrt{4-2x}}}$

Let $f(x)=x^2-2x+3.$ Find $f(-2),f(3),f(x+h),$ and ${\displaystyle \frac{f(x+h)-f(x)}{h}}.$

Let $f(x)=\sqrt{x}$ and $g(x)=x^2+1.$ Find each of the following.

1. f(g(x))

2. g(f(x))

3. f(f(x))

4. g(g(x))

Let $f(x)=\{\begin{array}{lll}3x+2& \text{if}& x\le 2\\ 4x-1& \text{if}& 2<x\le 3.\\ 6& \text{if}& x>3\end{array}$

1. Find f(1), f(3), and f(4).

2. Sketch the graph of $y=f(x).$

Let $f(x)=2x-3.$ Find $f{}^{-1}(x).$

Use transformations on $y=\sqrt{x}$ to sketch the graph of each function.

1. $f(x)=\sqrt{x+2}$

2. $g(x)=-2\sqrt{x+1}+3$

Use the Rational Zeros Test to list all possible rational zeros of $f(x)=2x^4-3x^2+5x-6.$

$f(x)=2x^2-4x+1$

$f(x)=-x^2+2x+3$

$f(x)={(x-1)}^2(x+2)$

$f(x)={\displaystyle \frac{x^2-1}{x^2-4}}$

Let $f(x)=x^4-3x^3+2x^2+2x-4.$ Given that $1+i$ is a zero of f, find all zeros of f.

Suppose that y varies as the square root of x and that $y=6$ when $x=4.$ Find y if $x=9.$

A drug manufactured by a pharmaceutical company is sold in bulk at a price of $150 per unit. The total production cost (in dollars) for x units in one week is

How many units of the drug must be manufactured and sold in a week to maximize the profit? What is the maximum profit?

The profit (in dollars) for a product is given by

where x is the number of units produced and sold. One breakeven point occurs when $x=10.$ Use synthetic division to find another break-even point for the product.