AP CALCULUS NAME_____________________________________
SUMMER PROJECT 2022-2023
SHOW ALL WORK FOR FULL CREDIT!
x −1
1. Find the domain and range of f (x) = .
x−4
Domain:______________
Range:_______________
2. Let f (x) = x − 2 and g(x) = x 6 + 2 , find the following (Hint: Use the text as a guide if needed):
a) ( f ( g ( x)) b) The domain of ( f ( g ( x))
c) ( g ( f ( x)) d) The domain of ( g ( f ( x))
⎧ 5 − 3x, x > 1
⎪
3. Sketch the graph of g(x) = ⎨ 3, x = 1
⎪ 2, x < 1
⎩
, ⎧ x−3
⎪ , x<3
4. Sketch the graph of f (x) = ⎨ x − 3
⎪ x, x > 3
⎩
5. One root of P( x) = x 3 + 2 x 2 - 5 x - 6 is x = -1 . Find the other roots algebraically.
x 4 + 3x 2 − 1
6. Divide using LONG DIVISION.
x2 + 5
7. A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet
of fencing. What is the maximum area that can be enclosed?
SUMMER PROJECT 2022-2023
SHOW ALL WORK FOR FULL CREDIT!
x −1
1. Find the domain and range of f (x) = .
x−4
Domain:______________
Range:_______________
2. Let f (x) = x − 2 and g(x) = x 6 + 2 , find the following (Hint: Use the text as a guide if needed):
a) ( f ( g ( x)) b) The domain of ( f ( g ( x))
c) ( g ( f ( x)) d) The domain of ( g ( f ( x))
⎧ 5 − 3x, x > 1
⎪
3. Sketch the graph of g(x) = ⎨ 3, x = 1
⎪ 2, x < 1
⎩
, ⎧ x−3
⎪ , x<3
4. Sketch the graph of f (x) = ⎨ x − 3
⎪ x, x > 3
⎩
5. One root of P( x) = x 3 + 2 x 2 - 5 x - 6 is x = -1 . Find the other roots algebraically.
x 4 + 3x 2 − 1
6. Divide using LONG DIVISION.
x2 + 5
7. A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet
of fencing. What is the maximum area that can be enclosed?
