Question

Need help graphing Y=(1.1)^x+sinx over the following intervals with an appropriate scale for y..?
1. -10 <(equal)x< (equal)10

2. -10<(equal)x<(equal)20

3 -10<(equal)x<(equal)30

4. -10<(equal)x<(equal)40

5. -10<(equal)x<(equal)50

**Also, why does the sine curve seem to disappear after graphing these intervals?

Answer 1

ok , so how did u draw them ?
or still wanna draw them ?

Answer 2

http://www.wolframalpha.com/input/?i=Y%3D%281.1%29^x%2Bsinx

Answer 3

@BSWan please help me draw them, I've been trying to put it on except but I can't seem to get it right

Answer 4

Things to consider:

\((1.1)^x\) is a geometric term, which tells you that as \(x\to-\infty\), \((1.1)^x\to0\). Meanwhile, \(\sin x\) remains, and that's why the sine curve is apparent to the left of the y-axis.

As \(x\to\infty\), \((1.1)^x\to\infty\) as well. This is because - if you consider the geometric sequence \((1.1)^n\), a divergent sequence - the common ratio is greater than 1, which makes every successive term in the sequence greater than the previous term.

To add to this, \(\sin x\) is bounded: \(-1\le\sin x\le1\). But \((1.1)^x\) is not. Because of this, \((1.1)^x\) will 'overtake' the value of sine, and so \(\sin x\) seems to disappear as \(x\) gets larger and larger.

As for graphing, I second the suggestion to use WA or some other graphing utility. Here are the plots for their appropriate domains; fortunately, WA picks out an appropriate scale for the range:

http://www.wolframalpha.com/input/?i=Plot%5B%281.1%29%5Ex%2BSin%5Bx%5D%2C%7Bx%2C-10%2C10%7D%5D

http://www.wolframalpha.com/input/?i=Plot%5B%281.1%29%5Ex%2BSin%5Bx%5D%2C%7Bx%2C-10%2C20%7D%5D

http://www.wolframalpha.com/input/?i=Plot%5B%281.1%29%5Ex%2BSin%5Bx%5D%2C%7Bx%2C-10%2C30%7D%5D

http://www.wolframalpha.com/input/?i=Plot%5B%281.1%29%5Ex%2BSin%5Bx%5D%2C%7Bx%2C-10%2C40%7D%5D

http://www.wolframalpha.com/input/?i=Plot%5B%281.1%29%5Ex%2BSin%5Bx%5D%2C%7Bx%2C-10%2C50%7D%5D

Answer 5

Thank you so much @sithsandgiggles, you helped me out so much!