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AP Calculus :: 2006-2007 :: Shubleka
Name______________________________ Page 1
Name:_________________________
PART ONE: EVEN OR ODD? 1. Examine the validity of the following statements: The composition of two odd functions is odd. The composition of two even function is even. The direct sum of an even and an odd function is odd. The quotient of two even functions is even. If true, prove the statement. If false, disprove it with a counterexample. Your response should start with formal definitions of odd and even functions.
PART TWO: NEW FUNCTIONS FROM OLD FUNCTIONS.
2. Consider the function f(x) defined by y x 3 2 x 1 . Write the equation of the new function in each of the following transformations: i. ii. iii. iv. v. vi. vii. viii. ix. x.
Stretch graph of f(x) vertically by a factor of 2. (5 points) Compress graph of f(x) vertically by a factor of 2. (5 points) Compress graph of f(x) horizontally by a factor of 3. (5 points) Stretch graph of f(x) horizontally by a factor of 3. (5 points) Reflect the graph of f(x) about the x-axis. (5 points) Reflect the graph of f(x) about the y axis. (5 points) Shift graph of f(x) vertically up by 9 units. (5 points) Shift graph of f(x) vertically down by 9 units. (5 points) Shift graph of f(x) horizontally to the right by 9 units. (5 points) Shift graph of f(x) horizontally to the left by 9 units. (5 points)
“Instead of having "answers" on a math test, they should just call them "impressions," and if you got a different "impression," so what, can't we all be brothers?”
Name______________________________ Page 1
Name:_________________________
PART ONE: EVEN OR ODD? 1. Examine the validity of the following statements: The composition of two odd functions is odd. The composition of two even function is even. The direct sum of an even and an odd function is odd. The quotient of two even functions is even. If true, prove the statement. If false, disprove it with a counterexample. Your response should start with formal definitions of odd and even functions.
PART TWO: NEW FUNCTIONS FROM OLD FUNCTIONS.
2. Consider the function f(x) defined by y x 3 2 x 1 . Write the equation of the new function in each of the following transformations: i. ii. iii. iv. v. vi. vii. viii. ix. x.
Stretch graph of f(x) vertically by a factor of 2. (5 points) Compress graph of f(x) vertically by a factor of 2. (5 points) Compress graph of f(x) horizontally by a factor of 3. (5 points) Stretch graph of f(x) horizontally by a factor of 3. (5 points) Reflect the graph of f(x) about the x-axis. (5 points) Reflect the graph of f(x) about the y axis. (5 points) Shift graph of f(x) vertically up by 9 units. (5 points) Shift graph of f(x) vertically down by 9 units. (5 points) Shift graph of f(x) horizontally to the right by 9 units. (5 points) Shift graph of f(x) horizontally to the left by 9 units. (5 points)
“Instead of having "answers" on a math test, they should just call them "impressions," and if you got a different "impression," so what, can't we all be brothers?”
