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MATH 1004 Study Guide - Quiz Guide: Maxima And Minima, Asymptote, Riemann Sum

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turquoisegnu128

1 Oct 2018

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Carleton University

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$MATH 1004 Full Course Notes$

MATH 1004 Full Course Notes

Document Summary

This test has two parts, the rst part has 8 multiple choice questions (each one 2. 5 marks) and the second part has 2 long answer questions. 1: what are the vertical and horizontal asymptotes of the function f (x) = 2 is a vertical asymptote and y = 1 (a) x = 3. 2 is a vertical asymptote and y = 3 is a horizontal asymptote. (b) x = 3 (c) x = 2. 3 is a vertical asymptote and y = 1. 3 is a horizontal asymptote. (d) x = 2. 3 is a vertical asymptote and there is no horizontal asymptote. 1 (e) y = is a horizontal asymptote and there is no vertical asymptote. 5(x 3)(x 4: y = 3, x = 3, x = 4. 5: x = 1, x = 2 are, x = 1, x = 2, has no asymptote, (6, 0) only, (3, 81) only, (0, 0) and (3, 81, (0, 0) only.

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Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. Use a transformation of the graph of y = x4 to graph the function. f(x) = (x + 8)4 Select the graph of f(x) = (x + 8)4. Find the vertical, horizontal, and oblique asymptotes, it any. or the given rational function. Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no oblique asymptote. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function has the given graph? Find the vertical, horizontal, and oblique asymptotes, if any. for the following rational function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Analyze the graph or the function. What is the domain of R(x)? {x|x - 14} {x|x 0. x 17, and x - 14} {x|x 0 and x - 14} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x - (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not, tell why not. Choose the correct answer below. Polynomial of degree 6 Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Not a polynomial because of the negative power of x

Show transcribed image text Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. Use a transformation of the graph of y = x4 to graph the function. f(x) = (x + 8)4 Select the graph of f(x) = (x + 8)4. Find the vertical, horizontal, and oblique asymptotes, it any. or the given rational function. Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no oblique asymptote. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function has the given graph? Find the vertical, horizontal, and oblique asymptotes, if any. for the following rational function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Analyze the graph or the function. What is the domain of R(x)? {x|x - 14} {x|x 0. x 17, and x - 14} {x|x 0 and x - 14} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x - (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not, tell why not. Choose the correct answer below. Polynomial of degree 6 Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Not a polynomial because of the negative power of x

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Algebra

Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.

Show transcribed image text Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.