The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. 1. Graph ( ) ( ) = − − f x x 3 2 4 using transformations. 2. For the polynomial function ( ) = + − − g x x x x 2 5 28 15, 3 2 (a) Determine the maximum number of real zeros that the function may have. (b) List the potential rational zeros. (c) Determine the real zeros of g. Factor g over the reals. (d) Find the x- and y-intercepts of the graph of g. (e) Determine whether the graph crosses or touches the x-axis at each x-intercept. (f) Find the power function that the graph of g resembles for large values of x . (g) Approximate the turning points on the graph of g. (h) Put all the information together to obtain the graph of g. 3. Find the complex zeros of ( ) = − + − f x x x x 4 25 100 3 2 . 4. Solve + − = − x x x 3 2 1 8 4 3 2 in the complex number system. In Problems 5 and 6, find the domain of each function. Find any horizontal, vertical, or oblique asymptotes. 5. ( ) = − + + − g x x x x x 2 14 24 6 40 2 2 6. ( ) = + − + r x x x x 2 3 1 2 7. Graph the function in Problem 6. Label all intercepts, vertical asymptotes, horizontal asymptotes, and oblique asymptotes. In Problems 8 and 9, write a function that meets the given conditions. 8. Fourth-degree polynomial function with real coefficients; zeros: − +i 2, 0, 3 . 9. Rational function; asymptotes: = = y x 2, 4; domain: { } ≠ ≠ x x x 4, 9 . 10. Use the Intermediate Value Theorem to show that the function ( ) = − − + f x x x 2 3 8 2 has at least one real zero on the interval [ ] 0, 4 . 11. Solve: + − < x x 2 3 2 12. Solve: + ≤ − x x x x 7 2 6 3 2 2 Chapter Test 1. Find the distance between the points ( ) = P 1, 3 and ( ) = − Q 4, 2 . 2. Solve the inequality ≥ x x 2 and graph the solution set. 3. Solve the inequality − < x x3 4 2 and graph the solution set. 4. Find a linear function with slope −3 that contains the point ( ) −1, 4 . Graph the function. 5. Find the equation of the line parallel to the line = + y x2 1 and containing the point ( ) 3, 5 . Express your answer in slope-intercept form, and graph the line. 6. Graph the equation = y x3. 7. Does the relation {( )( )( )( )} 3, 6 , 1, 3 , 2, 5 , 3, 8 represent a function? Why or why not? 8. Solve the equation − + = x x x 6 8 0 3 2 . 9. Solve the inequality + ≤ − x x 3 2 5 1 and graph the solution set. 10. Find the center and the radius of the circle + + − − = x x y y 4 2 4 0 2 2 Graph the circle. 11. For the equation = − y x x9 3 , determine the intercepts and test for symmetry. 12. Find an equation of the line perpendicular to − = x y 3 2 7 that contains the point ( ) 1, 5 . 13. Is the following the graph of a function? Why or why not? x y 14. For the function ( ) = + − f x x x5 2 2 , find (a) ( ) f 3 (b) ( ) − f x (c) ( ) −f x (d) ( ) f x3 (e) ( ) ( ) + − ≠ f x h f x h h 0 15. Given the function ( ) = + − f x x x 5 1 (a) What is the domain of f? (b) Is the point ( ) 2, 6 on the graph of f? (c) If = x 3, what is ( ) f x ? What point is on the graph of f? (d) If ( ) = f x 9, what is x? What point is on the graph of f? (e) Is f a polynomial or a rational function? 16. Graph the function ( ) = − + f x x3 7. 17. Graph ( ) = − + f x x x 2 4 1 2 by determining whether its graph is concave up or concave down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. 18. Find the average rate of change of ( ) = + + f x x x3 1 2 from 1 to 2. Use this result to find the equation of the secant line containing ( ) ( ) f 1, 1 and ( ) ( ) f 2, 2. Cumulative Review Cumulative Review 269
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