Math.docx

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