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1 25-Lance Burger 1 of 10 1/26/2017 9:34 AM Student: Date: Instructor: Lance Burger Course: Spring 2017 Math 75 - Burger Assignment: 25 1 Evaluate the following it Select the correct answer below and, if necessary, fill in the answer bo within your choice 3 A 3+ (Type an integer or a simplified fraction) 2 = B The it does not eist 2 Find the it sin Select the correct choice below and fill in any answer boes in your choice A sin 11 = 14 B The it does not eist (Simplify your answer) 3 Evaluate the following it Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A = B The it does not eist 4 Evaluate the following it sin Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A 174 sin = B The it does not eist

2 25-Lance Burger 2 of 10 1/26/2017 9:34 AM 5 Find the it of the polynomial p() as approaches 3 2 p() = The it of p() as approaches is 6 Evaluate f() and f() for the following rational function Then give the horizontal asymptote of f, if any f() = Evaluate f() Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A (Simplify your answer) = B The it does not eist and is neither nor Evaluate f() Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A (Simplify your answer) = B The it does not eist and is neither nor Give the horizontal asymptote of f, if any Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A The horizontal asymptote is (Type an equation Simplify your answer) B There is no horizontal asymptote

3 25-Lance Burger 3 of 10 1/26/2017 9:34 AM 7 Suppose p/q is a rational function where the degree of p is 1 greater than the degree of q Using polynomial long division, p() r() r() p/q can be written as =m+b+ where r/s is a rational function with the property q() s() s() 0 as ± This fact p() implies that q() m + b when is large The line y = m + b is an oblique (or slant) asymptote of p/q Complete parts (a) through (c) for the function f() = (a) Use polynomial long division to find the oblique asymptote of f Choose the correct answer below A y= 1 B y= 7 C y= +1 D y= +7 (b) Find the vertical asymptote of f Select the correct choice below, and, if necessary, fill in the answer bo to complete your choice A The vertical asymptote of f is = (Type an integer or a fraction) B There are no vertical asymptotes (c) Graph f and all of its asymptotes with a graphing utility Choose the correct graph below A B C D The window setting for all graphs is [-25,15] by [ 50,60]

4 25-Lance Burger 4 of 10 1/26/2017 9:34 AM 8 Complete the following steps for the given function ause polynomial long division to find the oblique asymptote of f b Find the vertical asymptotes of f cgraph f and all of its asymptotes with a graphing utility f() = a The oblique asymptote is y = b Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A The vertical asymptotes are = (Type an integer or a decimal Use a comma to separate answers as needed) B There are no vertical asymptotes c Graph the function f and all of its asymptotes using a graphing utility Choose the correct graph below A B C D

5 25-Lance Burger 5 of 10 1/26/2017 9:34 AM 9 Consider the function f() = (a) Evaluate f() and f(), then identify the horizontal asymptotes (b) Find the vertical asymptote For the vertical asymptote = a, evaluate f() and f() a a + (a) f() = f() = Identify the horizontal asymptotes Select the correct choice below and, if necessary, fill in the answer bo to complete your choice A The horizontal asymptote(s) is/are y = (Use a comma to separate answers as needed) B There are no horizontal asymptotes (b) Find the vertical asymptote For the vertical asymptote = a, evaluate f() and f() Select the correct choice a a + below and, if necessary, fill in the answer bo to complete your choice A The vertical asymptote is = The its at this vertical asymptote are f() = and f() = a a + B There is no vertical asymptote

6 25-Lance Burger 6 of 10 1/26/2017 9:34 AM 10 Consider the function f() = a Evaluate f() and f(), and then identify the horizontal asymptotes b Find the vertical asymptotes For each asymptote = a, evaluate f() and f() a a + a f() = (Simplify your answer) f() = (Simplify your answer) Identify all the horizontal asymptotes Select the correct choice below and fill in any answer boes within your choice A y= (Use a comma to separate answers as needed) B There are no horizontal asymptotes b Identify all the vertical asymptotes Select the correct choice below and fill in any answer boes within your choice A There are two vertical asymptotes The leftmost one is at = The its are f() = and a f() = a + The rightmost one is at = The its are f() = and a f() = a + B There is one vertical asymptote The asymptote is at = The its are f() = and a f() = a + C There are no vertical asymptotes

7 25-Lance Burger 7 of 10 1/26/2017 9:34 AM 11 Consider the function f() = 2 9 Complete parts a and b ( 3) a Evaluate f() and f(), and then identify the horizontal asymptotes 2 9 ( 3) = 2 9 ( 3) = Identify the horizontal asymptotes Select the correct choice below and, if necessary, fill in all the answer boes to complete your choice A The function has a horizontal asymptote at y = B The function has horizontal asymptotes at y = and y = (Use ascending order) C The function has no horizontal asymptote b Find the vertical asymptotes For each vertical asymptote = a, evaluate f() and f() a a + Select the correct choice below, and, if necessary, fill in all the answer boes to complete your choice A The function has a vertical asymptote at = The its at this vertical asymptote are f() = and f() = a a + B The vertical asymptote at = has the its f() and a = f() = The vertical asymptote at = has the its a + f() = and f() = a a + (Use ascending order) C The function has no vertical asymptote

8 25-Lance Burger 8 of 10 1/26/2017 9:34 AM 12 For the function f() = , find the following 1 (a) Evaluate f() and f(), and then identify the horizontal asymptotes (b) Find the vertical asymptote For the vertical asymptote = a, evaluate f() and f() a a + (a) f() = f() = Identify the horizontal asymptotes Choose the correct answer below A The horizontal asymptotes is/ are y = (Use a comma to separate answers as needed) B There are no horizontal asymptotes (b) Find the vertical asymptote For the vertical asymptote = a, evaluate f() and f() Select the correct a a + choice below and, if necessary, fill in the answer bo to complete your choice The vertical asymptote is = The its at this vertical asymptote are A f() = and f() = a a + B There is no vertical asymptote

9 25-Lance Burger 9 of 10 1/26/2017 9:34 AM 3 1 A 3+ (Type an integer or a simplified fraction) 2 = 3 sin 11 2 A = 0 (Simplify your answer) 14 3 A = 3 4 A sin = A (Simplify your answer) = A (Simplify your answer) = 0 A The horizontal asymptote is y=0 (Type an equation Simplify your answer) 7 B y = 7 A The vertical asymptote of f is = 7 (Type an integer or a fraction) C B There are no vertical asymptotes B

10 25-Lance Burger 10 of 10 1/26/2017 9:34 AM A The horizontal asymptote(s) is/are y = 2 (Use a comma to separate answers as needed) A The vertical asymptote is = 0 The its at this vertical asymptote are f() and a f() a + = A y = 2 (Use a comma to separate answers as needed) A There are two vertical asymptotes The leftmost one is at = 4 The its are f() = and f() = a a + The rightmost one is at = 5 The its are f() = and f() = a a A The function has a horizontal asymptote at y = 1 A The function has a vertical asymptote at = 0 The its at this vertical asymptote are f() and a a A The horizontal asymptotes is/ are y = 2, 2 (Use a comma to separate answers as needed) B There is no vertical asymptote