MAC 1105 College Algebra Sample Test 2 Chapter 2 1. Find the distance between points P(6, −8) and Q(3, 5). Leave answer in simplified radical form. 2. Find the midpoint of the segment connecting the points (16, −8) and (12, −17). 3. Consider: f ( x) = 3 x 2 − 4 x + 10 . a. f (3) Find: b. f ( x + 1) c. f ( x + h) − f ( x ) h 4. Write the equation of the line that passes through the point (−3, 2) and is a. parallel to the line 3x + 4 y = 8 b. perpendicular to the line 3x + 4 y = 8 Write your final answers in slope-intercept form. 5. Find the domain in each of the following. Write answers in interval notation. a. f ( x) = 7 x 2 − 5 x + 4 d. f ( x) = 3 x + 3 b. f ( x) = x − 3 e. f ( x) = c. f ( x) = 1 3− x 1 x +3 2 6. Find the center and radius of a circle whose equation is: x 2 − 4 x + y 2 + 8 y + 11 = 0 7. Write the standard form of the equation of the circle with center (−2, 8) and radius = 5. 8. For f ( x) = x 2 − 3 x and g ( x) = x + 3 , find each of the following: a. ( f + g ) x b. ( fg ) x c. ( g D f ) ( x) d. f ( g ( 3) ) 9. If f ( x ) = x +1 , 2x − 3 a. Find f −1 ( x ) 1/7/2010 b. Verify algebraically that f ( f −1 ( x ) ) = f −1 ( f ( x ) ) = x 10. Given: ⎧ 2 x + 3 if x ≥ −2 f ( x) = ⎨ , ⎩ − x − 2 if x < −2 a. f (−4) evaluate b. f (0) 11. Sketch the graphs on the same set of axes. Clearly mark the starting point plus two more ordered pairs on each function. a. f ( x) = x b. f ( x) = x − 3 c. f ( x) = x − 3 12. Sketch the graphs on the same set of axes. a. f ( x) = 1 x b. f ( x) = 1 x2 13. Determine whether the graph of each of the following functions is an even function, an odd function, or neither of these. Discuss symmetry. a. f ( x) = x 2 + 1 b. f ( x) = x3 + 1 c. f ( x) = x3 c. f ( x) = x + 1 14. Use this graph of the function f to answer the following questions. a. On what interval or intervals is f increasing? b. What is the relative minimum of the function? c. Evaluate f (1). 1/7/2010 15. Suppose the graph of f is given. Describe how each of the following functions can be obtained from the graph. Your answer may include words such as: shifts, reflects, stretches, up, down, left, right. a. y = f ( x) − 5 c. y = 2 f ( x) b. y = f ( x − 5) d. y = − f ( x) 16. The function f ( x) = 0.002 x 2 + 0.41x + 7.34 models the percent of the population in the United States, f ( x) , who graduated from college x years after 1960. a. Find f (40) b. Interpret f (40) 17. Data points (3, 276) and (5, 317) , shown in the table, fall on a straight line. x number of years after 1990. 3 5 y total of all Health Care Expenditures in Billions of Dollars 276 317 a. Write the equation of the line on which these measurements fall in slope-intercept form. b. Find the health care expenditures for 2000. 1/7/2010