Chapter 1: Fundamentals

Yes or No? If No, give a reason. Assume that$a$ and$b$are non-zero real numbers.

(a) Is the distance between any two different real numbers always positive?

(b) Is the distance between$a$ and$b$the same as the distance between role="math" localid="1649490736430" $b$ and$a$?

Write an equation that expresses the statement.

P is directly proportional to w.

If$S=\left\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\right\}.$ Determine which elements of satisfying the inequality.

$1-2x\ge 5x$

Find the domain of the expression.

$-x^4+x^3+9x$

Find all real solution

(a)$x+5=14-\frac{1}{2}x$

(b)$\frac{2x}{x+1}=\frac{2x-1}{x}$

(c)$x^2-x-12=0$

(d)$2x^2+4x+1=0$

(e)$\sqrt{3-\sqrt{x+5}}=2$

(f)$x^4-3x^2+2=0$

(g)$3|x-4|=10$

Express the given quantity in terms of the indicated variable.

The sum of three consecutive integers; n = middle integer of the three

The graph of an equation is shown below.

(a)The x-intercept(s) are$\text{\_\_\_\_}$, and the y-intercept(s) are$\text{\_\_\_\_}$.

(b)The graph is symmetric about the$\text{\_\_\_\_}$(x-axis/y-axis/origin)

An equation is given.

(a)Use a graphing calculator to graph the equation in the given viewing rectangle. (b) Find the x- and y-intercepts from the graph.

(c) Verify your answers to part (b) algebraically (from the equation).

$y=x^4-2x^3;\left[-2,3\right]\text{by}\left[-3,3\right]$

Using Slopes Verify the given geometric property.

Use slopes to verify $A\left(-3,-1\right),B\left(3,-3\right)$and $C\left(-9,8\right)$vertices of a right triangle or not.

Express the quantity without using absolute value

$\left|1-\sqrt{2}\right|$