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MTH 107 Chapter Notes - Chapter 5: Precalculus, Real Number, Even And Odd Functions

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30 Jun 2017

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University of Miami

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5. 1 polynomial functions and models notes: sterling. Identifying polynomial functions f (x) = anxn + an 1xx 1 + + a1x + a0. Graph : horizontal line with c as y intercept. Graph : a nonhorizontal and nonvertical line with a slope and y intercept. Example : y = x2 + 5x + 6. Power function f (x) = axn a 6= 0 n > 0. Zero of multiplicity r when the following: (x r)m is a factor of f, (x r)m+1 is not a factor of f. Zero of even multiplicity f (x)"s sign doesn"t change from one side of r to the other side, which will make the graph touch the x-axis at r. Zero of odd multiplicity f (x)"s sign does change from one side of r to the other side, which will make the graph cross the x-axis at r.

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Show transcribed image text Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 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. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 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 vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 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. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers

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