Chapter 1: Fundamentals

A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set.

Sketch the graph of region of the set $\left\{\left(x,y\right)\right\}|x\ge 2ory\ge 2$.

Sketch the region given by the set

$\left\{\left(x,y\right)\left|-4<x<4\text{and}-2<y<2\right.\right\}$

A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set.

Find the equation of the circle shown in figure

Proxima Centauri, the star nearest to our solar system, is 4.3 light-years away. Use the information in Exercise 87(a) to express this distance in miles.

If two electrical resistors with resistances $R_1$ and $R_2$ are connected in parallel (see the figure), then the total resistance R is given by

$R=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}}$

(a) Simplify the expression for R.

(b) If $R_1=10$ohms and$R_2=20$ohms, what is the total resistance R?

Factor the expression completely.

$12x^3+18x$

Find the real solutions of the equation $\sqrt{2x+1}+1=x$.

Factor the expression completely.

$30x^3+15x^4$