Unit I Wpp 6

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WPP 10: Unit L concepts 9-14

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WPP9: Unit L concepts 4-8

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Haiku

Football
 Intense
Amazing Sport
 Practice every day
 Play under Friday Night Lights
Win or lose football is a team sport

Student Problem 7 Unit K concept 10

So this concept is to show you how to write a repeating decimal as a rational number using geometric series. Well, basically you identify where the numbers are repeating and of corse this is infinite. So in my problem the number that repeats is 29 and the problem is .29292929 so the series will start .29+.0029+.000029+.00000029,..... We do this to find the "r" which in this case is .01. Then once we have a one and the r its possible to plug it in to the geometric series sum formula. So the sum formula for infinite series is a one over 1-r, or a one/1-r. then after we pug it in we will have 29/100 and 99/100 on the bottom. So we then switch them since you are dividing fractions the 100s cancel out and you are left with 29/99. Which can't be simplified so its your answer.

Student problem 2 unit I

First of all for this problem we will have no a or b. Since this problem consists of logs we will only have an H and a K. For this problem we can identify the h as -1 and the k as 3. In these types of log problems the h will be the vertical asymptote in this case x= -1. For the key points we can use any numbers to the right of the asymptote to plug in and make it a  more accurate graph. The x and y intercepts are always found by, for x pulg in y as 0 then solve to get your answer.Where as for the y-intercept you pulg in 0 for the x.

Well in this problem for the key points I used the x values 0,1,2,and 3. These are valid since they are to the right of the vertical asymptote. The Domain for this one will have restrictions due to the vertical asymptote, in this problem it will be (-1,infinty). Where as for the range we will have no restrictions which will be  (-infinity,infinity).

Student Problem unit I

This Unit consists of graphs. First of all we look at our equation and identify the a,b,h,and k. We know that the k will be the asymptote in this problem and in any problem. Since we have to find 4 points you suggested to start with the h as the 3rd one, as for this problem is -2. We go down a number up and up one number down, example -2 next "x" up is -3 then -4. The number next down from -2 in -1.

The x and y-intercepts are amoung the easiest to find, we simply substitute the y with a zero and solve. In this exanmple there is no x-intercept because as you can see the horizontal asymptote is 1. If you solve it you will get no solution. As for the y-intercept you substitue x for 0 and then solve in this problem we got y=13 so the y-intercept in (0,13). The Domain ask for all the x values available in this problem all of them are. The range will be otherwise since there is a horizontal aysmptote, in this problem it will be (1, infinity). Finally as for the graph we plug in the points we got when we subsituted the "x"s to get the new "y"s and get our graph. 

2. Describe what limit notation for horizontal asymptotes actually means. Well limit notation for horizontal asymptotes

5. Describe the conditions in which a graph can cross through an asymptote.

7. Describe how to write limit notation for vertical asymptotes and what the notation means.

9. Describe how to find the x-intercepts of a rational function. Include both the long way and the shortcut way; explaining the shortcut makes mathematical sense.

Post #8 Unit G

8. How do we find the y-intercept of a rational function? Does this need to be done in the original or simplified equation? We basically just substitute the x's from the original or simplified equation with a 0. solve and you will get your y-intercept or no intercept.

Post #6 Unit G

6. How do we find the appropriate place to plot a hole if the y-value is undefined when plugged into the original equation? Well this one is very simple question, you basically just plug in the x-value to the simplified equation to get the y-value. Then you will have an ordered pair which is easy to plot.

Post #4 Unit G

4. What is the difference between a graph having a vertical asymptote and a graph having a hole ? Well you have to factor both top and bottom and if anything cancels it will be a hole. Once you do that you then have to set the denominator equal to zero and solve. For a vertical asymptote the graphs can never ever cross through a vertical asymptote. A graph with a hole will have an open circle which means its a hole.

Post #3 Unit G

3. When does a graph have a slant asymptote? How would find the equation of the slant asymptote? Well first of all in order to have a slant asymptote the degree of the top has to be one degree bigger then the degree on the bottom. So you have to use long division and everything but your remainder is now the equation.

Post #1 Unit G

1. How do we know if a graph has a horizontal asymptote? What are the three options? Well first of all we have to compare the degrees of the numerator and denominator. Then if there is a bigger degree on bottom the asymptote is y=0. If they have the same degrees the asymptote is the ratio of the coefficients. Then lastly if the bigger degree is on top there will be no horizontal asymptote.We know a graph has a horizontal asymptote when the bigger degree is on the bottom. If this is so, y will equal zero. If the degree is the same, the asymptote is the ratio of the coefficient. If the bigger degree is on the top there will be no asymptote.