Curve Sketching Assignment 1. Find the intercepts of each function. a. f(a) = x2 + 2x - 15 [3 marks] by = =+10 x-5 [3 marks] c. f(x) = 8 - V4x2 - 46x + 108 [4 marks] 2. Find the domain of each function. a. y = [2 marks] by = 4x + 7x2 - 13x + 100 [1 mark] c. f(x) = V105 - 3x [3 marks] 3. Determine if each function is even, odd, or neither. a. f(x) = 1 (x3+27)2 [3 marks] by = a + 19x + 18 [3 marks] c. f (2) = 3 at23 [3 marks]4_Determine the vertical asymptote(s) of each function. a.y= I% [3 marks] e ] b. f( )W_azfs[\"ma\"' 5. Determine the horizontal asymptote, if any, of each function. ay=z>+ 222 61 markl x4 B2-T b.y = 545z 15 _ 9242 c. f(.?:) = 1g 3.7 [2 marks] [1 marks] 6. For each function determine the critical values, the intervals of increase and decrease, and the minimum and maximum points. a. f(a:} = 422 + 12z 7 [4 marks] b. f(z) = z* 9z + 24z 10 [4 marks] c.Y = #ila [4 marks] 7. Find the intervals of concavity and state the points of inflection in each function. a. f(a':} = z% 22% + z 2[4 marks] b. f(.?:) = If; [4 marks] 8. Using the second derivative test, find the maximum and minimum points for the function f(.r} = % 822 + 5[5 marks] 9. What conclusions can be made Iif: a. A function changes from a decreasing interval to an increasing interval at * = a? [1 mark] b. lim f(z) = ooand lim f(x) = co? [1 mark] z0t z0 C. f'(:) has a maximum at = a? [2 marks] 10. The function y = .,1':2 4x + 21 has a minimum at = 2. What are the coordinates of the minimum point? [2 marks] 11. When finding one-sided limits, what does ot represent? [1 mark] 12. When does a limit not exist? [3 marks] 13. What conditions must be met if a function is said to be continuous at a point (a, f(a))? [2 marks] 14. Use the curve sketching procedure to analyze the function f(z) = z? + 22 20z [12 marks] 2 15. Use the curve sketching procedure to analyze the function f(:c) = % [15 marks]