1. ACTIVITY 33 Review (Sections 3.1+3.2+3.3+3.4+3.5)

2. Problem 15: Let Evaluate

3. Problem 23: LetEvaluate

4. Problem 33: find:Let

6. Problems 39, 41, 47, and 53: Find the domain of each function. Since the numerator and denominator are polynomial, who’s domains are all real numbers, we need only be concerned with x – 3 = 0. That is x = 3 is the only real number not in the domain. Since the numerator and denominator are polynomial, who’s domains are all real numbers, we need only be concerned with x 2 – 1 = 0.

7. We must have a nonnegative real number under the square root. Consequently, the domain is all x’s such that Consequently, the critical numbers are x = 4 and x = -2

8. Problems 1 and 19: Sketch the graph of each function by first making a table of values. xy 02 12 2 22 -22

9. xy 02 10 4 22 34

10. Problems 41 Sketch the graph of the piecewise defined function

11. Problem 21: Determine the average rate of change of f(x) = x 3 − 4x 2 between x = 0 and x = 10.

12. Problem 23: Determine the average rate of change of f(x) = 3x 2 between x = 2 and x = 2 + h

13. Problems 5 and 7: Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. The graph is stretched vertically and flipped over the x – axis. The graph shrinks vertically and flipped over the x – axis. The graph is moved to the right 4 units and up ¾ units. The graph is moved to the left 4 units and down ¾ units.

15. Problem 33: Sketch the graph of f(x) = (x − 2) 2, not by plotting points, but by starting with the graph of a standard function and applying transformations.

16. Problem 47: Sketch the graph of f(x) = |x + 2| + 2, not by plotting points, but by starting with the graph of a standard function and applying transformations.

17. Problems 65 Determine whether the function f is even, odd, or neither. If f is even or odd, use symmetry to sketch the graph. Even functions are symmetric about the y – axis. Even

18. xy 0 undefined 11 21/4 1/24 1/39

19. Problem 13: Sketch the graph of y = 2x 2 +4x +3 and state the coordinates of its vertex and its intercepts. The vertex lies in the second quadrant and the parabola is going up so there can be no x – intercepts!

20. This 2 stretches the graph up

21. Problem 31: Find the maximum or minimum value of