In this blog post, I am going to compare and contrast asymptotes and holes in terms of equations and graphs.
https://www.wevideo.com/view/319474841?timelineId=317444594
Steps taken to find inverse functions First, you can switch the x to y and y to x. Then, if there is a number added or subtracted you can put the number on the other side, and switch the sign. Next, if there is a number in front of the x or y you have to divide it on both sides of the equal sign. Now you are done, congratulations! How to verify if two functions are inverses of each others If you got to functions, and you use one of them to find the inverse functions, you can verify if the other function is the inverse or not. Example when the inverse is a function f(x) = x + 6 x = y + 6 x - 6 = y f-1(y) = x - 6 Example when the inverse is not a function And that is how we do it!
Today, I am going to show you how to factor:
x^3+3x^2-54x First thing first, you have to find out if there is anything you can put outside a parenthesis. You can clearly see that there is at least an x in every term. Therefore you can put that outside, and the function will look like this: x(x^2+3x-54) Furthermore you have to find out two numbers you can multiply to get -54. Here you can make a list, if you want to. 9 * -6 -6 * 9 -18 * 3 -3 * 18 -27 * 2 -2 * 27 Now you can try to set in the numbers in two parentheses, and test if it is the correct answer. x(x-6)(x+9) To be sure it is the right numbers you can multiply and see what the answer is. I found out that this is correct. So this is how you factor. How is factoring and solving related? I have learned three different ways to solve a system of two equations with two unknowns. In this blog I am going to describe each methods, explain which is my favorite and why. Substitution method You are given two equations: 2x+y=4 3x+2y=1 First you have to solve the equation for y in terms of x. 2x+y=4 y=4-2x Then you have to use the other equation to solve the x in terms of y. Afterward, you can fill in what you found out y equals, and solve the equation. 3x+2y=1 3x=1-2y 3x=1-2(4-2x) 3x=1-8+4x 3x-4x=-7 -x=-7 |:(-1) x=7 Then you have to find y, by putting 7 in for x. y=4-2(7) y=4-14 y=-10 The solution is (7,-10) Elimination method You are given two equations: 4x-y=16 3x-y=10 First you have to subtract 4x and 3x, and then you have to subtract -y and -y, and subtract 16 and 10. Then you have: x=6 Now you have to find y, by substituting 6 for x in either original equation. 3(6)-y=10 18-y=10 y=18-10 y=8 The solution is (6,8) Graphing method On this method you can make a graph, and make the lines from the two given equations. For example you can use desmos.com. Then you just have to look at the exact coordinates of the point where the lines intersect from the graph. Here you can see an example. I prefer using the substitution method, because that is the one I have used since I first learned about this. I think it is a fun method, when I get the right answer. However, using desmos is the easiest, but if I did not get the chance to use desmos, I would not prefer to draw the graph by hand.
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March 2015
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