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anonymous
 one year ago
Help with graphing problem? will award medal for best answer!
Graphs of irrational functions show things about extraneous solutions. Let f(x) = x  √x2
a. find f(11), f(6), f(2), f(2), and f(0).
b. plot the graph of the function.
c. what is the domain of x if f(x) is to be a real number?
d. show that there are no real values of x for which f(x)=0.
please help! If you could plot the graph and answer all that would be awesome! Im so confused
anonymous
 one year ago
Help with graphing problem? will award medal for best answer! Graphs of irrational functions show things about extraneous solutions. Let f(x) = x  √x2 a. find f(11), f(6), f(2), f(2), and f(0). b. plot the graph of the function. c. what is the domain of x if f(x) is to be a real number? d. show that there are no real values of x for which f(x)=0. please help! If you could plot the graph and answer all that would be awesome! Im so confused

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let f(x) = x  √x2 a. to find each of these answers, you need to "plug and chug" each value into the function. For example f(11) = 11  √112 = 11  √9 = 11  3 = __8__ f(6) = 6  √62 = 6  √4 = 6  2 = ______ Just do the same with the rest of them. Wherever the x is in the function, replace it with the value given in the parentheses. b. plot the graph of the function. An easy way to plot a graph, is to use find data points or use data points you already know and then basically "connectthe dots". Using your answers from part (a) is a great way to do this. For example, with f(11), we were able to find that when x = 11, the function (or y) = 8. Therefore, one point in your coordinate graph will be (x, y) = (11, 8). Use the rest of your answers from part (a) to finish. c. what is the domain of x if f(x) is to be a real number? The key to answering this part is recognizing and knowing the definition of a "real number". A real number is defined as including all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2. Basically it encompasses all types of numbers. ) http://www.scimathmn.org/stemtc/sites/default/files/images/frameworks/math/8.1.1A/image131.jpg). Secondly, it is important to know the definition of domain this refers to all the possible numbers that x could be. Lastly, one other important rule to keep in mind, is this: you may not have a negative number under a square root (when this happens it is known as an imaginary number). Therefore, x may not be less than 2. Hence, x must be between (the domain is) +2 and infinity ("greater than or equal to 2"). d. show that there are no real values of x for which f(x)=0. This is a simple proof done by assuming that there is in fact a value for x for which f(x)=0. Therefore, given the function f(x) = x  √x2 you set up the equation as: 0= x  √x2 and solve for x. You will find that it does not work and will end up with an inequality/false statement. After arriving to a false statement you could state. "QED" or "therefore there are no real values of x for which f(x)=0.
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