College Algebra – Practice Test 1
Please note that the actual test will be shorter.
1. Find the distance between the pair of points:
• (4, 6) and (5, 9)
• (−1, −2) and (3, 1)
2. Find an equation for a circle with center (−1, 2) and radius = 3
3. State the vertical-Line Test.
4. Find equations of the following lines:
• slope= 2 and point= (−1, −3)
• points (−6, −1) and (2, −10)
5. Write a slope-intercept equation for the line 3x + y = 1. Then write an equation for a line
passing through (1, 0) that is parallel to the given line. Then write an equation for a line
passing through (1, 0) that is perpendicular to the given line.
6. Solve
• −x + 1 = 1 − x
• 3(x + 1) = 5 − 2(3x + 4)
• 8x − 7 < 6x + 3
• −3 < 1 − 2x < 3
7. Graph the following functions, then indicate intervals where they are increasing or decreasing,
and any relative max or min.
• f (x) = (x − 1)2
• f (x) = |x| − 1
8. Given f (x) = 2x − 1 and g(x) = 2x + 5, find f + g, f − g, f g and f /g.
and g(x) = 2x, find f ◦ g and g ◦ f , and the domain of each.
√
10. Refer to page 194 of the textbook. sketch y = x − 1 + 1 and y = −2(x − 1)3
9. Given f (x) =
1
1−x