Dalia Isabel Gonzalez rocha math1010spring2016-90 3 WeBWorK assignment number WBWK-05 is due : 02/15/2016 at 11:59pm MST. This assignment is on linear functions and other functions in general. Thinking is when your mouth stops talking and your brain keeps working. Dennis the Menace 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. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ^ 3 instead of 8, sin(3 pi/2)instead of -1, e ^ (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) ^ 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. f (10) = f (13) = 1. (1 pt) Let the function f be dened by f (x) = 3x Then f ( 8) = 5. (1 pt) Use the table of values given below to solve the following exercises. 2. and f ( 7) = x 3 2 1 0 1 2 3 2. (1 pt) Suppose f (x) = 3x 2. Then A. f (1) = , B. f (t) = , a) Which equation corresponds to the points given in the table? C. f (x2 ) = 3. (2 pts) Evaluate the function f (x) = values: 13 x 19+x at the indicated f (2) = f(1) = 2 f (a) = 1) = 8 2 < 5x + 6 5 4. (2 pts) Let f (x) = : 7 x A. y = x2 B. y = |x| C. y = 2 x D. y = |x| b) Does the graph of the equation pass through the origin? (Enter: Yes or No ) Answer: c) At which point does the graph of the equation cross the x-axis? Answer: d) At which point does the graph of the equation cross the y-axis? Answer: f ( 2) = f (a y 5 4 3 2 1 0 1 x<5 5 x 10> 10 6. (1 pt) Evaluate the function g(x) = p 9 x2 + 3 for x = p 13 without using a calculator. Simplify your answer as much as possible. f (0) = f (5) = f (6) = p g( 13) = 1 7. (1 pt) Express the rule \"Subtract 20, then square\" as the function 12. (1 pt) Find the domain and range of the function p y = 49 x. f (x) = For this problem, enter the answer using INEQUALITY NOTATION. If the domain includes all real numbers, enter all real numbers. . x 8. (1 pt) f (x) = 3 + 8 can be expressed in words as \"Add 8, then divide by 3\". Is this statement true? Your answer is (input Yes or No): Domain: . Range: 9. (1 pt) Express the rule \"Multiply by 4, then add 8\" as the function f (x) = HINT FOR DOMAIN AND RANGE: Algebraically: For which x is the square root dened? This give you the domain. Which values will f(x) be? This gives you the range. . p 10. (1 pt) The domain of the function 2x 4 is [ , ). If the answer is , input -innity; if the answer is , input innity. Graphically: You are able to graph this by hand. Look at your graph and identify the domain and range. For the domain, your variable is x. For the range, your variable is y. 11. (1 pt) Find the domain and range of the function. y = x2 + 5. 13. (1 pt) The domain of the function 14x2 + 14 is ( , ). If the answer is , input -innity; if the answer is , input innity. For this problem, enter the answer using INEQUALITY NOTATION. If the domain includes all real numbers, enter all real numbers. 14. (2 pts) If possible, nd the indicated values for the rational function. If the value does not exist, enter Does not exist . 2x2 + x 1 f (x) = x 3 a) f (6) = b) f (3) = c) f (0) = For this problem, enter the domain using INEQUALITY NOTATION or INTERVAL NOTATION. For help with the notation, consult the link . If the domain includes all real numbers, enter \"all real numbers\" (no extra spaces, without quotation marks). Domain: Range: HINT FOR DOMAIN AND RANGE: Algebraically: Which values of x can you use? This give you the domain. Which values will f(x) be? This gives you the range. d) Find the domain of f : Graphically: You are able to graph this by hand. Look at your graph and identify the domain and range. HINT FOR DOMAIN: Algebraically: For which x is the fraction undened? For the domain, your variable is x. For the range, your variable is y. 2 Graphically: You are able to nd the domain algebraically....but you can use a graphing calculator to see what the function looks like and why the domain is what it is (search \"graphing calculator online\" for web-based graphing calculators). Note, this is an exception to the \"NO CALCULATOR\" rule. In this class, you would NOT be expected to graph this function by hand, but if you were given a picture of it, you would be expected to answer questions about it, like stating its domain and range. Let the function f be dened by f (x) = 6x + 7 . 9x + 7 The domain of f contains all real numbers x except x = Hint: Never divide by zero. 15. (2 pts) If possible, nd the indicated values for the rational function. If the value does not exist, enter Does not exist . 2x2 x f (x) = 2 x +4 18. (1 pt) Click on the graphs to view enlarged ones Enter Yes or No in each answer space below to indicate whether the corresponding curve denes y as a function of x. a) f (0) = b) f ( 4) = c) f ( 1) = For this problem, enter the domain using INEQUALITY NOTATION or INTERVAL NOTATION. For help with the notation, consult the link . If the domain includes all real numbers, enter \"all real numbers\" (no extra spaces, without quotation marks). d) Find the domain of f : 1. HINT FOR DOMAIN: Algebraically: For which x is the denominator 0? (Beware - this is a bit tricky) Graphically: You can nd the domain without seeing the graph of this function, but if you are stuck, it may be useful to use a graphing calculator to see what the function looks like (search \"graphing calculator online\" for web-based graphing calculators). Note, this is an exception to the \"NO CALCULATOR\" rule. In this class, you would NOT be expected to graph this function by hand, but if you were given a picture of it, you would be expected to answer questions about it, like stating its domain and range. 2. 16. (1 pt) Find the domain of f (x) = px1 2 . Give the answer in INTERVAL NOTATION. a) What is the domain of f (x)? 17. (1 pt) The domain is the set of real numbers at which the function can be evaluated, and the range is the set of all possible outputs. To determine the domain ask yourself at what points the function can NOT be evaluated. Usually this is because of an undened operation, which practically speaking means dividing by zero, or extracting the square root of a negative number. 3. 3 A 4. B C D 5. Which one of the graphs is a function? A. B. C. D. 6. 20. (2 pts) Suppose the function g is given by the following table of values. To be marked correct, you must type \"yes\" and \"no\