Cumulative Review 187 1. Find the distance between the points P 1, 3 ( ) = − and Q 4, 2. ( ) = − Find the midpoint of the line segment from P to Q. 2. Which points are on the graph of y x x3 1? 3 = − + (a) 2, 1 ( ) − − (b) 2, 3 ( ) (c) 3, 1 ( ) 3. Solve the inequality x5 3 0 + ≥ and graph the solution set. 4. Find the equation of the line containing the points 1, 4 ( ) − and 2, 2. ( ) − Express your answer in slope–intercept form and graph the line. 5. Find the equation of the line perpendicular to the line y x2 1 = + and containing the point 3, 5 . ( ) Express your answer in slope–intercept form and graph both lines. 6. Graph the equation x y x y 4 8 5 0. 2 2 + − + − = 7. Does the following relation represent a function? 3,8 , 1,3 , 2,5 , 3,8 . ( ) ( ) ( ) ( ) { } − 8. For the function f defined by f x x x4 1, 2 ( ) = − + find: (a) f 2( ) (b) f x f 2 ( ) ( ) + (c) f x ( ) − (d) f x( ) − (e) f x 2 ( ) + (f) f x h f x h h , 0 ( ) ( ) + − ≠ 9. Find the domain of h z z z 3 1 6 7 . ( ) = − − 10. Is the following graph the graph of a function? y x 11. Consider the function f x x x 4 . ( ) = + (a) Is the point 1, 1 4 ( ) on the graph of f ? (b) If x 2, = − what is f x ? ( ) What point is on the graph of f ? (c) If f x 2, ( ) = what is x? What point is on the graph of f ? Cumulative Review 12. Is the function f x x x2 1 2 ( ) = + even, odd, or neither? 13. Approximate the local maximum values and local minimum values of f x x x5 1 3 ( ) = − + on 4, 4 . [ ] − Determine where the function is increasing and where it is decreasing. 14. If f x x3 5 ( ) = + and g x x2 1: ( ) = + (a) Solve f x g x . ( ) ( ) = (b) Solve f x g x . ( ) ( ) > 15. Consider the graph below of the function f. (a) Find the domain and the range of f. (b) Find the intercepts. (c) Is the graph of f symmetric with respect to the x-axis, the y-axis, or the origin? (d) Find f 2 . ( ) (e) For what value(s) of x is f x 3? ( ) = (f) Solve f x 0. ( ) < (g) Graph y f x 2. ( ) = + (h) Graph y f x . ( ) = − (i) Graph y f x 2 . ( ) = (j) Is f even, odd, or neither? (k) Find the interval(s) on which f is increasing. (4, 3) (24, 3) (22, 1) (21, 0) (0, 21) x y 25 5 4 24 (1, 0) (2, 1)
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