Fiesta 3: Ap Calculus Ab 2009 - 2010

AP Calculus AB | Fiesta #3 | Shubleka     

Name: ____________________ Period______ You may not use a graphing calculator on this quiz. Show all your work, justify your answers, and present your work neatly on separate sheets.

1. Determine whether the function is increasing, decreasing, or neither. a) f ( x) = 3− x b) f ( x) = x 1+1 2

c) g (t ) = t 2 + t d) g (t ) = t 3 + t 2. Determine whether the function is even, odd, or neither. Write a short proof of your claim in each case. a) f ( x) = x 4 − 3x 2 b) f ( x) = sin ( x + 1) c) f ( x) = 2− x

2

3. Find the roots of f ( x) = x 4 − 4 x 2 and sketch its graph. Discuss the increasing/decreasing behavior of this function. 4. Let f ( x ) = cos x and g ( x) = x −1 .Compute the composite functions f D g and g D f , and find their domains. 5. Let f ( x ) = cos x . Sketch the graph of y = 2 f ( 13 x − π4 ) for 0 ≤ x ≤ 6π .