I have been wracking my brain and can not figure this out so I've broken down and am asking this question on here in hopes that someone can show me how to do this.
I need to figure out if this sine graph has been translated left or right and by how many units.
I can't figure it out from the information provided by the graph. I'm stuck on this idea that I need to figure out the period but I can't do that because I can't determine what the x-values of the min. and max. are. Well, it's looks like the x-value of the min. is 0 but I can't figure out the max.
At any rate, anyone know how to do this?
Period = distance between two peaks or maxima. It appears the peaks or maxima are at a little more than $ \pm 3$ so $ x =\pm \pi \approx \pm 3.14$ would be a reasonable guess. Then period = $ \pi - (- \pi) = 2\pi $, unchanged from the basix function sin$(x)$.
Amplitude = (max - min)/2 = (1 - (-1))/2 = 1, also inchanged from the basic function.
Sin$(x)$ = 0 at x = 0, and sin$(x)$ is increasing at $x = 0.$
The two points visible on this graph which fit both criteria are at x close to or a little above 1.5, and $x$ close to -4.6 or -4.7. Since it appears we are dealing with radian measure, a period of $2 \pi$ and maxima and minima at multiples of pi, then a reasonable assumption would be that $x = 0$ and $f(x)$ is increasing ($f'(x)$ positive) at $x = \pi/2 \approx 1.57$ and at $x = - 3 \pi/2 \approx -4.71 $
Thus the graph could be sin$(x)$ shifted $\pi/2$ to the right OR $3 \pi/2$ to the left. (Since the period is $2\pi$ adding any multiple of $2\pi$ to the phase shift will give a correct result.)
The function would be $f(x) = \sin (x - \pi/2) $ OR $f(x) = \sin (x + 3\pi/2)$