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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.