[SPLIT] rule to go from y = sin(x) to y = 0.667sin0.5x + 1

[Daimeera]

I've run into yet another problem.

I understand stretches and transformations now, I'm pretty sure. I can figure out mapping rules--or at least I could until now. But now, I'm stuck.

I'm supposed to find the mapping rule to go from y = sin(x) to y = 0.667sin0.5x + 1

(In this case, it was easier to type them up as decimals rather than fractions, but you get the idea).

Now, I'm assuming that (x, y) -> (something x-1, y) but I can't figure out how to find the stretch. I've tried multiplying numbers and adding them but I can't seem to make sense of it, nor find the correct response.

I also created a table with the new values, but it didn't much help me (x=0, y=1; x=90, y=1.47; x=180, y=1.67; x=270, y=1.47; x=360, y=1) and compared it to the original which, with the same values for x, ends up with y values of 0; 1; 0; -1; 0.

I haven't been able to find any number that makes sense to me that accounts for the difference in the two tables.

So, how does one deal with the two fractions in this equation? I've tried everything I can think of (and yes, I've graphed it, as well, with no luck still), but I'm out of ideas.

Thank you SO much in advance, and I'm sorry for the barrage of questions.

 

[tkhunny]

y = sin(x) to y = 0.667sin0.5x + 1

Normally, you should
Sadly, this one is a little troubled. I cannot tell from what you have written what you mean. Three possibilities come to mind.

1) y = 0.667sin(0.5x) + 1 <== This is what you wrote.

2) y = 0.667sin(0.5x + 1)

3) y = 0.667sin(0.5(x + 1))

Use more parentheses to clarify meaning.

 

[Daimeera]

That's what was confusing me, too, actually. There were no parentheses in the book, it was simply \(\displaystyle y=\frac2 3 \sin \frac1 2x + 1\)

Perhaps this is different from what I wrote down, however?

I don't know. It's confusing me to no end, the lack of parentheses alone, and then the two fractions even moreso.