Calculus

Math 150 Exam 1

1. (1 pt) If f(x) = x2 – 2x + 4, evaluate the difference quotient

f(a + h) – f(a)

         h

 

2. (4 pts) Find the domain and range of the function. Write your answer in interval notation.

(a) f(x) =     3__   

                2x – 1

                   _______

(b) g(x) = √(16 – x4)

(c) h(x) = x2 + 6x + 9

(d) f(x) = 3 + sin 2t

3. (3 pts) Use transformations to sketch the graph of the function. Start from the graph of the corresponding basic function. You must show all the transformations.

y = – (x – 2)3 + 4

4. (1 pt) Graph the function.

               –x + 1       if x < 0  

f(x) = {2x – 1 if x ≥ 0 

5. (4 pts) If f(x) = 1 / x and g(x) = x2 – 9, find the functions and their domains.

(a) f ◦ g

(b) g ◦ f

(c) f ◦ f

(d) g ◦ g

                                                                        ________

6. (1 pt) Express the function F(x) = 1 / √(x + √(x))  as a composition of three functions.

7. (1 pt) If f(x) = x / π + sin x, find f -1(1).

8. (1 pt) Find the inverse function of f(x) = (x + 2) / (2x – 1).

9. (4 pts) Simplify each expression.

(a) 2x2(3x5)2

(b) (2x-2)-3 x-3

(c) 3a3/2 a1/2 / a-1

(d) (a1/2 b1/2) / (ab)1/2

10. (2 pts) Solve each equation for x.

(a) 4x = 23x

(b) tan x = 1

11. (4 pts) Determine whether f is even, odd, or neither.

(a) f(x) = |x| + 1

(b) f(x) = x3 – 1 

(c) f(x) = –sin x

(d) f(x) = cos 2x

12. (4 pts) If f(x) = 2x + 1 and g(x) = 1 – √(x), find

(a) (f + g) (x) and its domain

(b) (f – g) (x) and its domain

(c) (f ∙ g) (x) and its domain

(d) (f / g) (x) and its domain