MATH 126 TEST 1 SAMPLE

Transcription

1 NAME: / 60 = % MATH 16 TEST 1 SAMPLE NOTE: The actual exam will only have 13 questions. The different parts of each question (part A, B, etc.) are variations. Know how to do all the variations on this exam. 1A.) (6 pts) Given: A = ( 4, 3) and B = (8, ), find the following: i.) The distance from A to B. i. ii.) The midpoint of a line segment containing A and B. ii. iii.) The slope of a line passing through A and B. iii. 1B.) (6 pts) Given: A = (4, 3) and B = (6, 4), find the following: i.) The distance from A to B. i.

2 ii.) The midpoint of a line segment containing A and B. ii. iii.) The slope of a line passing through A and B. iii. A.) (5 pts) Identify the center and radius: x + y + 4x + y 11 = 0 Then graph. Center: Radius: 11 B.) (5 pts) Identify the center and radius: x + y x + y = 0 4 Then graph. Center: Radius:

3 x 4 3A.) (3 pts) Find the domain: f ( x) = 3A. 7x 3 Write your answer in interval notation. 3 4x 3B.) (3 pts) Find the domain: f ( x) = 3B. 30 Write your answer in interval notation. 5x 3C.) (3 pts) Find the domain: f ( x) = 3C. x 5x + 6 Write your answer in interval notation. 4A.) (4 pts) Find the equation, in slope-intercept form, of a line that is perpendicular to the line 5x + 4y + 8 = 0 and passes through ( 5, 4). Graph your equation. Equation:

4 4B.) (4 pts) Find the equation, in slope-intercept form, of a line that is parallel to the line x + y + 4 = 0 and passes through ( 1, ). Graph your equation. Equation: 5A.) (4 pts) A company plans to manufacture a certain product with fixed costs of $ It will cost $140 to manufacture each unit, and each will be sold for $300. Write a function that describes the profit, P, in terms of units sold x. 5A. 5B.) (4 pts) Suppose that a company purchases a new car for $8000. After 3 years, the car is worth $ Write a linear function that expressed the value, V, of the car as a function of its age, t. 5B.

5 6A.) (5 pts) Graph using transformations: y = x Start with the base graph (library function) and then graph each successive transformation. The final graph will be your graph of y = x Base Graph Final Graph 6B.) (5pts) Graph using transformations: y = 1 x. Start with the base graph (library function) and then graph each successive transformation. The final graph will be your graph of y = 1 x. Base Graph Final Graph 7A.) (5 pts) Indicate what kind of symmetry (x-axis, y-axis, origin) 9 x this graph has: y =. Also find its x and y intercepts. 3x Sym: x-int: y-int:

6 7B.) (5 pts) Indicate what kind of symmetry (x-axis, y-axis, origin) this graph has: x y = 4. Also find its x and y intercepts. Sym: x-int: y-int: 8A. (4 pts) Determine algebraically whether or neither. 3 x f ( x) = is even, odd, 8A. 3 x 9 8B. (4 pts) Determine algebraically whether or neither. 3 f ( x) = x 3 is even, odd, 8A.

7 9A.) (4 pts) Find the difference quotient for f ( x + h) f ( x) using. h = by 9A. f ( x) 3x x 9B.) (4 pts) Find the difference quotient for f ( x) = x 4 by 9B. 3 f ( x + h) f ( x) using. h 10A.) (6 pts) Given 3 + x if 3 x < 0 f ( x) = 3 if x = 0 find the following and graph. x if x > 0 a.) f (0) : b.) 3 f : c.) f (9) : d.) f ( 4) :

8 10B.) (6 pts) Given 1 + x if x < 0 f ( x) = find the following and graph. x if x 0 a.) f (0) : b.) f ( 3) : c.) f : 3 d.) 1 f : 11A.) (4 pts) Use the graph of f ( x) below to answer the questions. a.) Find f (5) 11a. b.) Find all values of x such that f ( x) = 3. c.) Find the domain. d.) Find the range. e.) Interval(s) of decreasing f.) List the number at which the graph has relative max. g.) What is the value of the relative minimum? h.) How many times does the line y = 5/ intersect f? 11b. 11c. 11d. 11e. 11f. 11g. 11h.

9 11B.) (4 pts) Use the graph of f ( x) below to answer the questions. a.) Find f ( 4) 11a. b.) Find all values of x such that f ( x) = 0. c.) Find the domain. d.) Find the range. e.) Interval(s) of increasing f.) List the number at which the graph has relative min. g.) What is the value of the relative maximum? h.) How many times does the line y = 1/ intersect f? 11b. 11c. 11d. 11e. 11f. 11g. 11h. 1A.) (6 pts) Let 1 f ( x) = and x 3 3 g ( x) = x + i.) Find ( f o g)(0) if possible. i. ii.) Find ( g o f )( x). Write as a single fraction. ii.

10 iii.) Find ( f o g)( x). Simplify. iii. 1B.) (6 pts) Let f ( x) = x + 3 and g ( x) = x 4 i.) Find ( f o g)(1) if possible. i. ii.) Find ( g o f )( x). Factor your answer. ii. iii.) Find ( f o g)( x). Factor your answer. iii.

11 13A.) (4 pts) Find f 1 5 ( x) if f ( x) = 3x + 5. You do NOT need to do 13A. a check to verify your answer. 13B.) (4 pts) Find 1 ( x x f ) if f ( x) =. You do NOT need to do 13B. x + 3 a check to verify your answer.

12 MATH 16 TEST 1 REVIEW PROBS Section Problems 1.1 # # #75 84, 87 94, #9 16, #37 44, 51 60, (part a only) 1.6 #15 17, 19 4, 63 7, 75, 76 (no stretches or compressions) 1.7 #7 18, 33 46, 47, 48, 61 66, #37 44, 47 58, 65 76, 3.1 #41 50 The test will be closed-book, and no notes are allowed (no notecards are allowed either). The exam will consist of problems similar to the ones on the sample test and the above list of review problems.