Math_112_Fall_2010.jkovalsky.Lesson_08_-_Introduction_to_Functions

Math_112_Fall_2010.jkovalsky.Lesson_08_-_Introduction_to_Functions

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Unformatted text preview: JORDAN KOVALSKY Math - 112 Spring 2010 WeBWorK Assignment Lesson 08 - Introduction to Functions Due Date: 09/24/2010 at 11:59pm CDT. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. You can use the Feedback button on each problem page to send e-mail to the course instructors. 1. (1 pt) Determine the domain of the function y = 3x - 8. Enter your answer using interval notation. Domain is Determine the domain of the function y = 1/(3x - 8). Enter your answer using interval notation. Domain is Determine the domain of the function y = 3x - 8. Enter your answer using interval notation. Domain is 1 Determine the domain of the function y = . Enter your 3x - 8 answer using interval notation. Domain is Determine the domain of the function y = 3 3x - 8. Enter your answer using interval notation. Domain is Correct Answers: (-infinity,infinity) (-infinity,-3) U (-3,infinity) [-3,infinity) (-3,infinity) (-infinity,infinity) 3. (1 pt) Determine the domain of the function y = -5x - 1. Enter your answer using interval notation. Domain is Determine the domain of the function y = 1/(-5x - 1). Enter your answer using interval notation. Domain is Determine the domain of the function y = -5x - 1. Enter your answer using interval notation. Domain is 1 Determine the domain of the function y = . Enter -5x - 1 Correct Answers: your answer using interval notation. (-infinity,infinity) Domain is (-infinity,2.66666666666667) U (2.66666666666667,infinity) Determine the domain of the function y = 3 -5x - 1. Enter your [2.66666666666667,infinity) answer using interval notation. (2.66666666666667,infinity) Domain is (-infinity,infinity) 2. (1 pt) Determine the domain of the function y = 2x + 6. Enter your answer using interval notation. Domain is Determine the domain of the function y = 1/(2x + 6). Enter your answer using interval notation. Domain is Determine the domain of the function y = 2x + 6. Enter your answer using interval notation. Domain is 1 . Enter your Determine the domain of the function y = 2x + 6 answer using interval notation. Domain is Determine the domain of the function y = 3 2x + 6. Enter your answer using interval notation. Domain is 1 Correct Answers: (-infinity,infinity) (-infinity,-0.2) U (-0.2,infinity) (-infinity,-0.2] (-infinity,-0.2) (-infinity,infinity) 4. (1 pt) Determine the domain and the range of the function g(x) = 5x - 10 . Enter your answer using interval notation. 4x - 4 Domain is Range is Correct Answers: (-infinity,1) U (1,infinity) (-infinity,1.25) U (1.25,infinity) 5. (1 pt) Each of the following rules defines a function with domain the set of all real numbers. Express each rule in the form of an equation. EXAMPLE: The rule For each real number, compute its square can be written y = x2 . For each real number, subtract 6 and then square the result. y= For each real number, compute its square and then subtract 6 from the result. y= For each real number, multiply it by 6 and then square the result. y= For each real number, compute its square and then multiply the result by 6. y= 8. (1 pt) H(0) No 5/8 Let g(x) = 5x2 . Find the following. g(7x) = 7g(x) = g(x2 ) = [g(x)]2 = g(x/7) = g(x)/7 = For checking: No two answers are the same. Correct Answers: 5 * 7**2 * x**2 5 * 7 * x**2 5 * x**4 5**2 * x**4 5/49*x^2 5/7*x^2 Correct Answers: (x-6)**2 x**2 - 6 (6*x)**2 6 * x**2 9. (1 pt) 6. (1 pt) Let H(x) = 1 - 4x2 . Find the following. H( 8) = H(3/7) = H(x + 2) = H(x + h) = Each of the following rules defines a function with domain equal to the set of all real numbers. Express each rule in words. y = 2x3 + 1 y = 2(x + 1)3 y = (2x + 1)3 y = (2x)3 + 1 Turn in your answers to your instructor. Correct Answers: -31 13 / 49 - 4 x**2 - 16 * x - 15 1 - 4 * x**2 - 8 * x * h - 4 h**2 10. (1 pt) 7. (1 pt) Let H(x) = 1 - x + x2 - x3 . Which number is larger, H(0) or H(1)? ? Find H(1/2). Does H(1/2) + H(1/2) = H(1)? ? H(1/2) = If f (x) = 5x + 5, does f (1 + 8) = f (1) + f (8)? ? If f (x) = 5x, does f (1 + 8) = f (1) + f (8)? ? If f (x) = x, does f (1 + 8) = f (1) + f (8)? ? Correct Answers: 2 Correct Answers: No Yes No 11. (1 pt) Let h(t) = (2t - 5)/(t - 5). In each case, find all the real number solutions (if any) for the given equation. If there are no solutions, enter "NONE". h(t) = 15 t= h(t) = 2 t= h(t) = 0 t= 14. (1 pt) 3 * x**2 + 6 * x * h + 3 * h**2 - 2 * x - 2 * h Compute each expression, given that the functions f and g are defined as f (x) = 4x - 1 and g(x) = x2 - 5x - 6. ( f g)(x) = ( f g)(1/4) = Correct Answers: 4 x**3 - 21 * x**2 + -19 * x + 6 0 Correct Answers: -70 / -13 NONE 5 / 2 15. (1 pt) 12. (1 pt) Let T (x) = 5x2 - 4x. Find and simplify T (x + 3). T (x + 3) = Compute each expression, given that the functions g and m are defined as g(x) = x2 - 2x - 2 and m(x) = x2 - 2. (g + m)(x) = (g + m)(x) - (g - m)(x) = Correct Answers: 5 * x^2 + 26 * x + 33 Correct Answers: 2 * x**2 - 2 * x - 4 2 * x**2 - 4 16. (1 pt) 13. (1 pt) Let T (x) = 3x2 - 2x. Find and simplify T (x + h). T (x + h) = Simplify 81y12 + 9y6 = Note: Do not include absolute values in your answer, even though they may be appropriate. Correct Answers: c Generated by the WeBWorK system WeBWorK Team, Department of Mathematics, University of Rochester Correct Answers: 3*y^3*sqrt(9*y^6+1) 3 ...
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