***ONLY USE THE INFORMATION GIVEN TO ANSWER THE QUESTIONS ANY OUTSIDE FORMULAS, OR WAYS OF SOLVING THE ANSWER WILL BE REJECTED MUST BE DONE ON PAPER WITH WORK SHOWN!!!!***

To find the x-intercepts of a function set y = 0 and solve for x.

To find the y-intercepts of a function set x = 0 and solve for y.

When finding the?domain, remember:

• The denominator (bottom) of a fraction?cannot be zero
• The number under a square root sign?must be positive?in this section

REMEMBER YOUR f(x) and Lim functions and Continuity of Functions.MUST BE ON PAPER AND DONOT PUTAN EXPLANATION WITH WORK

Curve Sketching Procedure

1. Domain

2. Intercepts

3. Symmetry

4. Asymptotes

5. Intervals of increase or decrease

6. Maximum and minimum points

7. Intervals of concavity

8. Points of inflection

9. Sketch the curve

MUST DO!! MUST BE ON PAPER AND DONOT PUTAN EXPLANATION WITH WORK

8. Using the second derivative test, find the maximum and minimum points for the function f (x)=x* -8x2 +5 9. What conclusion can be made if: a. A function changes from a decreasing interval to an increasing interval. b. lim f (x ) = - and lim f (x )=0 x- 0 10. If the minimum of the function y= x2 -4x +21 occurs at x = 2, what are the coordinates of the minimum point?? 11. When finding one-sided limits what does 0' imply? 12. When does a limit not exist? 13. What conditions must be met if a function is said to be continuous? 14. Use the curve sketching procedure to analyze the function. a. y=x'+x -20x b. veltx 1-x24. Determine the vertical asymptote(s). x' +5x -7 a. y = x2 -3x -28 b. f ( x ) = x3 +4x3-4x+6 x3 +2x2 -5x -6 5. Determine the horizontal asymptote. x*+2x2 -6 a. y b. y = _x* +3x3 +x2 -7 x5 -3x3 +8 2x2 c. f (x)= x' +3x -4 6. For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points. a. f (x) =4x2 +12x -7 b. f (x=x' -9x2 +24x-10 x 2 C. V=- x2 +2x -15 7. Find the intervals of concavity for the function and state the points of inflection. a. f (x)=x* -2x3+x-2 b. f ( x ) = - xz -41. Find the intercepts of the function. a. f (x)=x2 +2x -15 x+10 b. V=. x -5 2. State the domain of the function. x* -3x +2 a. y = x-4 b. y =4x* +7x