how do you find the range and y intercept of y=3sin(2x)+2

Question

jim_thompson5910 · Answer

to find the y intercept, plug in x = 0 and evaluate

anonymous · Answer

y=2?

jim_thompson5910 · Answer

yes

jim_thompson5910 · Answer

the range of sin(x) spans from -1 to +1

in other words,

$$\Large -1 \le \sin(x) \le 1$$

the x can be replaced with anything you want, so let's replace x with 2x

$$\Large -1 \le \sin(2x) \le 1$$

jim_thompson5910 · Answer

we can then multiply every side by 3

$$\Large -1*3 \le 3*\sin(2x) \le 3*1$$

$$\Large -3 \le 3\sin(2x) \le 3$$

jim_thompson5910 · Answer

and then finally add to 2 all sides

$$\Large -3+2 \le 3\sin(2x)+2 \le 3+2$$
$$\Large -1 \le 3\sin(2x)+2 \le 5$$

so the range of y = 3*sin(2x)+2 spans from -1 to +5 (including both endpoints)

anonymous · Answer

Just to clarify, we must assume always that -1<sin(x)<1?

jim_thompson5910 · Answer

yes sin(x) is a function that bounces up and down. It doesn't go past y = 1 or y = -1. It's boxed in so to speak in terms of the y direction

jim_thompson5910 · Answer

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