Page 65 - Calculus Demystified

CHAPTER 1
52
√ √ √ Basics
2
4. Plot each of the points (2, −4), (−6, 3), (π, π ), (− 5, 8), ( 2π, −3),
(1/3, −19/4) on a pair of cartesian coordinate axes. Label each point.
5. Plot each of these planar loci on a separate set of axes.
2
(a) {(x, y): y = 2x − 3}
2
2
(b) {(x, y): x + y = 9}
3
(c) y = x + x
3
(d) x = y + y
2
(e) x = y − y 3
4
2
(f) x + y = 3
6. Plot each of these regions in the plane.
2
2
(a) {(x, y): x + y < 4}
2
(b) {(x, y): y> x }
3
(c) {(x, y): y< x }
(d) {(x, y): x ≥ 2y + 3}
(e) {(x, y): y ≤ x + 1}
(f) {(x, y): 2x + y ≥ 1}
7. Calculate the slope of each of the following lines:
(a) The line through the points (−5, 6) and (2, 4)
(b) The line perpendicular to the line through (1, 2) and (3, 4)
(c) The line 2y + 3x = 6
x − 4y
(d) The line = 6
x + y
(e) The line through the points (1, 1) and (−8, 9)
(f) The line x − y = 4
8. Write the equation of each of the following lines.

(a) The line parallel to 3x + 8y =−9 and passing through the point
(4, −9).
(b) The line perpendicular to x + y = 2 and passing through the point
(−4, −8).
(c) The line passing through the point (4, 6) and having slope −8.
(d) The line passing through (−6, 4) and (2, 3).
(e) The line passing through the origin and having slope 6.
(f) The line perpendicular to x = 3y − 7 and passing through (−4, 7).
9. Graph each of the lines in Exercise 8 on its own set of axes. Label your
graphs.
10. Which of the following is a function and which is not? Give a reason in
each case.