MATH 1LS3 Study Guide - Final Guide: Differentiation Rules, Dot Product, Chain Rule

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

Determine the end behavior of the following function as x → +oo and as X →-00. f(x) = 5x-4 As x → +00,f(x) → Equation Editor | sin (a) x/ 血Help -00 As X → -00,f(x) → Equation Editor d' sin (a) Help -00

XYour answer is incorrect. Try again. Link to question with no attempts available What families does the function 1(x) = Assume a, b and c are positive constants. Select all that apply. ( )" belong to? Power Rational O Exponential Polynomial

Assume/x) is continuous on an interval around x = 0, except possibly at x = 0. What does the table of values suggest as the integer value of lim f(x)? x 1-0. I -0.01 | 0.01 | 0.1 ТР8.987P8.999|98.999 8.987 lim f(x) seems to be equal to 99 Does the limit definitely have this value? Select all the options that apply Yes, because the function is continuous on an interval around x = 0. Yes, the table shows this is the limit with certainty O No, we do not know the limit or sure because for values of χ c se to 0 different from those the table the va a eso c m ght not approach the given value. O No, the limit may not exist, even though the table seems to hint it does No, the function could be approaching, for example, 99.00001 or 98.9999 Yes, the table indicates that for values of x close to O different from those in the table, the values of f(x) will approach the given value.

Chapter 1, Section 1.5, Question 020 Your answer is incorrect. Try again. Find a possible formula for the graph -20 π 20π Enclose arguments of functions in parentheses. For example, sin (2x) f(x)=1 6-sin(pix/10)

Given f(x) = 3x2 - 2 and g(x) = 3 - 1/2 x2: find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Simplify your answer.) find the following expressions, (f.g)(4) (g.f)(2) (f.f)(l) (g.g)(0) (fog)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) Given f(x) = |x| and g(x) =9/x2+3, find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Type an integer or a simplified fraction.) For the function on the right determine whether the function is one-to-one. Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes Find the inverse of the one-to-one function. State the domain and range of the inverse function. {(10,-8), (-13,-10), (-9,2), (-8,11), (-10,1)} Which of the following is the inverse function? {(-10,1), (-8,11), (-9,2), (-13,- 10), (10,-8)} {(-8,10), (-10,-13), (2,-9), (11,-8), (1,-10)} {(-8,-10), (-10,-8), (2,-9), (11,-13), (1,10)} {(-10,8), (13,10), (9,-2), (8,-11), (10,-1)} Consider the functions f(x) = - 3x + 7 and g(x) = -1/3(x - 7). Find f(g(x)). Find g(f(x)). Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Consider the functions f(x) = 3x - 15 and g(x) = x/3 + 5. Find f(g(x)). Find g(f(x)) Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Match the graph to one of the following functions. y = 6x y = 6-x y = -6x y = -6-x y = 6x_ 1 y = 6x-1 Which function is represented by the graph? (Type A, B, C, D, E, F, G, or H.) Begin with the graph of y = ex and use transformations to graph the following function. Determine the domain, range, and horizontal asymptote of die function. f(x) = 8e-x Choose the correct graph below. Solve the equation. 4x.2x2=162 x = (Use a comma to separate answers as needed.) If 4-x = 5;what does 42x equal? 42x = (Type a reduced fraction.)