Assignment 10: 3.2.44, 3.2.59, and TMP(10b)
I just spent the first part of my extremely exciting Friday night doing my math homework, and I had trouble with a couple problems...
For number 44 in 3.2, we were to answer questions about a piecewise g(x) function. I was able to answer it, and did so by graphing, but my calculator wouldn't let me type the rule -1<=x<=2 into the "y=" screen. When we are graphing things like y= 2x-3 | x<-1 or y= |x|-5 | -1<=x<=2 can we only include a one-sided inequality? Am I typing something wrong?
For number 59 in 3.2, I knew that to find the domain, I had to solve (x-9)^2 <= 9 (since what's inside the square root sign must be greater than or equal to zero). These were the steps of my solution:
(x-9)^2<=9
|x-9|<=sq.rt.(9)
x-9<=3 and x-9<= -3
x<=6 and x<=12
However, the solution the book gave is [6,12], meaning that I should have gotten x>=6. Where should I have switched the direction of the inequality sign? I am sure there's an easier way to solve this on a calculator, but I'm just curious to find my mistake.
For 10b on the TMP sheet, I am just really confused about how to approach it. In the third row of the table, I got a final result of y=(x^2/4)-5. And if I made the changes given in 10b, the final result would be y=(0.5(x-k))^2+x-4. I tried setting these two equations equal to one another on my calculator and solving for k, but I got a complicated sq.rt. answer with x involved. Did anyone find an actual numerical value for k?
Thanks guys
For number 44 in 3.2, we were to answer questions about a piecewise g(x) function. I was able to answer it, and did so by graphing, but my calculator wouldn't let me type the rule -1<=x<=2 into the "y=" screen. When we are graphing things like y= 2x-3 | x<-1 or y= |x|-5 | -1<=x<=2 can we only include a one-sided inequality? Am I typing something wrong?
For number 59 in 3.2, I knew that to find the domain, I had to solve (x-9)^2 <= 9 (since what's inside the square root sign must be greater than or equal to zero). These were the steps of my solution:
(x-9)^2<=9
|x-9|<=sq.rt.(9)
x-9<=3 and x-9<= -3
x<=6 and x<=12
However, the solution the book gave is [6,12], meaning that I should have gotten x>=6. Where should I have switched the direction of the inequality sign? I am sure there's an easier way to solve this on a calculator, but I'm just curious to find my mistake.
For 10b on the TMP sheet, I am just really confused about how to approach it. In the third row of the table, I got a final result of y=(x^2/4)-5. And if I made the changes given in 10b, the final result would be y=(0.5(x-k))^2+x-4. I tried setting these two equations equal to one another on my calculator and solving for k, but I got a complicated sq.rt. answer with x involved. Did anyone find an actual numerical value for k?
Thanks guys
posted by Casey Blue at 7:07 PM
4 Comments:
For number 44 in 3.2, your issue lies with the "and" operator. Just type in "|x>=1 and x<=2" and it will graph it in the interval you want.
For #59, I don't really know which part you did wrong so you got a different answer. I did 9-(x-9)^2>=0, and it is factorable, -(x-12)*(x-6)>=0, then you draw it on the "number line"(I don't know what is it called) to find the domain 6<=x<=12.
For TMP 10b, I also got a answer with x in it.
thanks guys
For TMP I got a radical including x also when i solved for k.
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