Practice Problems
Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers.
Answers
1. (a) –3/4 (b) 1/2 (c) 0 (d) 2 (e) undefined
3. (a) (b) (c) (if )
(d) (if ) (e) (if )
5. (a)
(c) decreasing, since the numerator remains constant at 5000 while the denominator increases.
7. The restaurant is 4 blocks south and 2 blocks east. The distance is blocks.
9. feet, so .
11. The equation of the line through and is or . Substituting and into the equation for the line, we get which equals 2 for every value of a, so the point with
and is on the line through P and Q for every value of a.
13. (a) so the lines are perpendicular.
(b) Because 20 units of x-values are physically wider on the screen than 20 units of y-values.
(c) Set the window so (xmax - xmin) ≈ 1.7 (ymax - ymin).
19. The distance between the centers is .
(c) 0 (they intersect)
21. Find , and compare the value to r: P is
outside the circle if
23. A point lies on the circle if and only if its distance from is . So
P is on the circle if and only if or .
(b) undefined (vertical line)
(d) 0 (horizontal line)
27. (a) distance ≈ 2.22.
(b) Distance ≈ 2.24.
(c) (by inspection) 3 units which occurs at the point (5, 3).
29. (a) If , we may solve for y: . The slope is the coefficient of x: .
(b) The required slope is B/A (the negative reciprocal of –A/B) so the equation is or .