Page 20 - Calculus Demystified

CHAPTER 1
Basics
The point Z is 5 units to the right of the y-axis and 4 units above the x-axis. 7
Therefore its coordinates are (5, 4).
The point W is 6 units to the left of the y-axis and 5 units below the x-axis.
Therefore its coordinates are (−6, −5).
You Try It: Sketch the points (3, −5), (2, 4), (π, π/3) on a set of axes. Sketch
the set {(x, y): x = 3} on another set of axes.
EXAMPLE 1.6
Sketch the set of points ={(x, y): y = 3}. Sketch the set of points k =
{(x, y): x =−4}.
SOLUTION
The set consists of all points with y-coordinate equal to 3. This is the set
of all points that lie 3 units above the x-axis. We exhibit in Fig. 1.9. It is a
horizontal line.

Fig. 1.9

The set k consists of all points with x-coordinate equal to −4. This is the set
of all points that lie 4 units to the left of the y-axis. We exhibit k in Fig. 1.10.
It is a vertical line.
EXAMPLE 1.7
Sketch the set of points S ={(x, y): x> 2} on a pair of coordinate axes.

SOLUTION
Notice that the set S contains all points with x-coordinate greater than 2.
These will be all points to the right of the vertical line x = 2. That set is
exhibited in Fig. 1.11.

You Try It: Sketch the set {(x, y): x + y< 4}.

You Try It: Identify the set (using set builder notation) that is shown in Fig. 1.12.