Math 110 Test # 1. The set of real numbers in both of the intervals [0, 2) and ( 1, 0] is equal to. Question 1. (F) [ 1, 2) (G) (2, ) (H) [ 1, 2]

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1 Friday July 8, 00 Jacek Szmigielski Math 0 Test # Fill in the bubbles that correspond to the correct answers. No aids: no calculators, closed book. You are not permitted to consult with your fellow students in any way. Time: 60 minutes. Question. The set of real numbers in both of the intervals [0, ) and (, 0] is equal to (, ) (B) (, ) (C) (, ) (D) {0} (E) {} (F) [, ) (G) (, ) (H) [, ] Question. Let n be an integer greater than or equal to. The number of integers in the interval ( n, n + ) is n (B) n (C) n (D) n + (E) n (F) (G) n + (H) 0 Question. The largest value of x y for x, y [, 6] is 4 (B) (C) 4 (D) 0 (E) 6 (F) 8 (G) 0 (H) Question 4. Solve the equality x + =. The solution set is, 7 (B), (C), (D), (E), 7 (F), (G), (H), Question. Solve the inequality x + >. The solution set is (, ) (B) (, ) (, ) (C) (, ) (, ) (D) (, ) (, ) (E) (, ] (F) [, ) (G) (, ] [, ) (H) (, ) (, ) Question 6. Solve the inequality x + x + < 0. The solution set is (, ) (B) { } (C) (, ) (D) {±} (E) (F) [, ] (G) (, ] [, ) (H) {0}

2 Question 7. The set of x such that 0 < x < π and ( + sin x)(x ) = 0 is { π} (B) {, π} (C) (D) {, π} (E) {π} (F) {} (G) {, π } (H) {, π } Question 8. The length of the longest side in the triangle with vertices (0, ), (, ) and (, ) is (F) 4 (B) (C) 6 (D) 7 (E) 8 9 (G) 0 (H) Question 9. is The value of m for which the lines x + y = 44 and mx 4y = are perpendicular (B) 0 (C) (F) π (G) (H) 0 44 (D) 44 (E). Question 0. The line going through the points (.,.9), (.7,.9) has slope equal to. (B).7 (C) (D).7 (E) (F).9 (G).9 (H) Question. The value of tan π 4 is (B) (C) (D) 0 (E) (F) (G) (H) Question. The value of tan x if cos x = and π < x < π is (B) (F) π (G) (C) (D) (E) (H) 8 Question. If f(x) = x + then the value of f() is (B) 0 (C) x 8 (D) 6x + 4 (E) 4 (F) 8 (G) 6 (H) 6 Question 4. If f(x) = x + then the set of x such that f(x) > is [, ) (B) (, ) (C) [, ) (D) [, ) (E) (, ) (F) (, ) (G) [0, ] (H) (, )

3 y y=f(x) x The remaining questions refer to the graph above, which is the graph of a function called f(x). Question. The domain of f is (, ) (B) (, ] (C) [, ] (D) (, ) (E) (, ) (F) [0, ] (G) [, ] (H) [, ] Question 6. The value of f() is (B) (C) (D) (E) 0 (F) (G) (H) does not exist Question 7. The set of x such that f(x) 0 is [, ) [, ](B) (, 0) (C) [, ) (, ](D) [0, ) (E) (0, ) (F) ( 4, ] (G) (, 0] (H) [, ] Question 8. The range of f is (, 0] (B) (, ) (C) [, ] (D) (, ) (E) [, ] (F) [, ) (G) (, ) (, ) (H) (, ] [, ) Question 9. The set of x such that f(x) = 0 is {0, } (B) {} (C) { } (D) {0,, } (E) {, } (F) (G) {0} (H) (, ) Question 0. If f(x) = and x < then x is (B) (C) 0, (D) (E) 0,, (F) 0 (G) 0, (H) none Question. On exactly one of the following sets it is true that f is increasing. Which one? [, ] (B) [, 0] (C) [, 0] {} (D) (, ) (E) (0, ) (F) (, ) (G) {, } (H) (, 0)

4 Next 6 questions refer to the functions f(x) = x and g(x) = x. Question. The value of (f + g)(6) is 4 (B) 6 (C) 8 (D) 0 (E) (F) 4 (G) 6 (H) 8 Question. The value of g f() is 7 (B) (C) 0 (D) (E) (F) (G) 0 (H) Question 4. The value of x such that f g(x) = g f(x) + is 7 7 (B) (C) (F) 0 (G) 7 (H) (D) (E) Question. The domain of the function f g is (, ) (, ) (B) (, ) (C) (, ) (D) [, ) (E) { } (F) (, ] (, ) (G) (, ) (H) [, ) Question 6. The domain of the function f g is [ 4, ) (B) (, ) (C) (, 4 ] (D) [0, ) (E) (0, ) (F) ( 4, ) (G) (, 0) (H) (, 0] Question 7. The value of f (4) is 4 (B) 6 (C) 8 (D) 0 (E) (F) 4 (G) (H) Question 8. The exact value of log 9 ( ) is (B) (C) (D) (E) (F) (G) (H) Question 9. The value of x for which x = is: log + (B) ln (C) ln + (D) log + (E) (F) log + (G) (H) log + Question 0. The exact value of log log 4+log is 4 (B) 0 (C) (D) (E) (F) (G) (H) Question. If the function f(x) = x then the inverse function f (x) is: log x + log x (B) log (log x) (C) log (log x) (D) log (log x) (E) log log x (F) log log x (G) x (H) log x

5 The following questions refer to the above figure. Graph A of the figure is the graph of a function y = f(x), while the other graphs are graphs of y = a + bf(cx + d), for various values of a, b, c and d. Question. Graph B is the graph of the function f(x 4) (B) 4f(x) (C) f( x) (D) f( x) 4 (E) f(x 4) + 4 (F) f(x + 4) (G) f(x) + 4 (H) f(4 x) Question. Graph C is the graph of the function f(x ) + (B) f(x + 4) (C) f(x ) + (D) f(x + 8) (E) f(x 4) (F) f( x 8) (G) f(x 4) (H) f(x 4) Question 4. Graph D is the graph of the function f( x) (B) f(x 4) (C) f(x + 4) + 4 (D) f(x) (E) f(x + 4) (F) f(x 4) + 4 (G) f(x) + 4 (H) f( x) Question. Graph E is the graph of the function f(x) (B) f(x 4) (C) f(x + 4) + 4 f(x) (E) f(x + 4) (F) f(x 4) + 4 (G) f(x) + 4 (H) f( x)

6 Question 6. Graph F is the graph of the function f(x + ) + (B) f(x + ) 4 (C) f(x + ) + (D) f(x ) + 4 (E) f(x ) (F) f(x ) + (G) f(x) + 4 (H) f(x )