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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