MATH 170, Test 2 Sample Exam
... Answer: No; x is raised to the -1 power. In the following problem, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. 41. Zeros: -1, 1, 3; degree 3. Answer: f(x) = x3 – 3x2 – x + 3 for a = 1. ...
... Answer: No; x is raised to the -1 power. In the following problem, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. 41. Zeros: -1, 1, 3; degree 3. Answer: f(x) = x3 – 3x2 – x + 3 for a = 1. ...
2.6 Rational Functions (slides, 4 to 1)
... behavior” of rational functions: what happens for x-values far away from 0, towards the “ends” of our graph? ...
... behavior” of rational functions: what happens for x-values far away from 0, towards the “ends” of our graph? ...
AP Calculus BC - 4J Blog Server
... R by taking x sufficiently close to c (but not equal to c). If the limit exists and is a real number, then the common notation is lim f ( x ) = R x→c ...
... R by taking x sufficiently close to c (but not equal to c). If the limit exists and is a real number, then the common notation is lim f ( x ) = R x→c ...
Midterm 3 - GMU Math
... 5 Find the absolute maximum and absolute minimum (if any) of the function f (x) = x3 − 3x2 − 9x + 10 on the interval −2 ≤ x ≤ 2. Solution. From the derivative f ′ (x) = 3x2 − 6x − 9 = 3(x + 1)(x − 3) we see that the critical numbers are x = −1 and x = 3. Of these, only x = −1 lies in the interval − ...
... 5 Find the absolute maximum and absolute minimum (if any) of the function f (x) = x3 − 3x2 − 9x + 10 on the interval −2 ≤ x ≤ 2. Solution. From the derivative f ′ (x) = 3x2 − 6x − 9 = 3(x + 1)(x − 3) we see that the critical numbers are x = −1 and x = 3. Of these, only x = −1 lies in the interval − ...
Final Exam Review
... C.3 61. An open box is made from a 10-cm by 20-cm piece of aluminum by cutting a square from each corner and folding up the edges. The area of the resulting base is 90 cm2. What is the length of the sides of the squares? C.2 62. A small business purchases a piece of equipment for $25,000. After 10 y ...
... C.3 61. An open box is made from a 10-cm by 20-cm piece of aluminum by cutting a square from each corner and folding up the edges. The area of the resulting base is 90 cm2. What is the length of the sides of the squares? C.2 62. A small business purchases a piece of equipment for $25,000. After 10 y ...
Ch5Review - AP Calculus AB/BC Overview
... A person has 340 yards of fencing for enclosing two separate fields, one of which is to be a rectangle twice as long as it is wide and the other a square. The square field must contain at least 100 square yards and the rectangular one must contain at least 800 square yards. a) If x is the width of t ...
... A person has 340 yards of fencing for enclosing two separate fields, one of which is to be a rectangle twice as long as it is wide and the other a square. The square field must contain at least 100 square yards and the rectangular one must contain at least 800 square yards. a) If x is the width of t ...
ALGEBRAIC GEOMETRY (1) Consider the function y in the function
... (3) Consider the function xy in the function field of E : y 2 = x3 + x2 . Can you determine whether f is defined at P = (0, 0)? Is g = f 2 defined at P ? Parametrizing suggests that f should be defined at P and that f (P ) = 0. This is misleading, however: assume that xy = hg with h(P ) 6= 0. Rewrit ...
... (3) Consider the function xy in the function field of E : y 2 = x3 + x2 . Can you determine whether f is defined at P = (0, 0)? Is g = f 2 defined at P ? Parametrizing suggests that f should be defined at P and that f (P ) = 0. This is misleading, however: assume that xy = hg with h(P ) 6= 0. Rewrit ...
Course: Math 8 Quarter 1 - Zanesville City Schools
... congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 5. Use informal arguments to establish facts about the angle sum and exterior angle ...
... congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 5. Use informal arguments to establish facts about the angle sum and exterior angle ...
Please show your work and circle your final answers
... The length of a piece of cardboard is five times its width. To make a box with an open lid, a seven inch piece was cut from each corner and the sides were folded up. If x represents the width of the cardboard, answer the following questions: a) What is the restriction on x? b) Determine the volume o ...
... The length of a piece of cardboard is five times its width. To make a box with an open lid, a seven inch piece was cut from each corner and the sides were folded up. If x represents the width of the cardboard, answer the following questions: a) What is the restriction on x? b) Determine the volume o ...
as x a - nvhsprecalculusconn
... A function is increasing on an interval if for any x1, and x2 in the interval, where x1 < x2, then f (x1) < f (x2). A function is decreasing on an interval if for any x1, and x2 in the interval, where x1 < x2, then f (x1) > f (x2). A function is constant on an interval if for any x1, and x2 in the i ...
... A function is increasing on an interval if for any x1, and x2 in the interval, where x1 < x2, then f (x1) < f (x2). A function is decreasing on an interval if for any x1, and x2 in the interval, where x1 < x2, then f (x1) > f (x2). A function is constant on an interval if for any x1, and x2 in the i ...
A2 C1 Test Review
... transformed point? (5,-1); vertical shift 3 units down and horizontal shift 4 units left _______________________________ 3. What numbers complete the table of the transformed function? Reflection across y-axis X ...
... transformed point? (5,-1); vertical shift 3 units down and horizontal shift 4 units left _______________________________ 3. What numbers complete the table of the transformed function? Reflection across y-axis X ...
Higher-Degree Polynomial Functions
... Note that although some functions may have asymptotes you will not always be asked to find or interpret them (read the questions carefully and answer only what you are asked about). For the rational function: Vertical asymptote occurs in x-values where ...
... Note that although some functions may have asymptotes you will not always be asked to find or interpret them (read the questions carefully and answer only what you are asked about). For the rational function: Vertical asymptote occurs in x-values where ...
Asymptote
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity.The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means ""not falling together"", from ἀ priv. + σύν ""together"" + πτωτ-ός ""fallen"". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound.More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.