Step-by-step explanation:
I think I'm a little too late to answer this question, but I'm still going to give you a basic sin function to show you where to find these things :)
[tex]f(x)=a sin (px)+s[/tex]
I put the variables corresponding to their appropriate word.
(a=amplitude, p=period, s=shift)
You can find the amplitude in front of the sin (or cos, tan, cot, etc). The amplitude is always the first number presented in a trig function.
You find the period by taking the number paired with the x and dividing 2π by it. ( [tex]\frac{2\pi }{p}[/tex] ) In this case, you're looking for a period of [tex]\frac{\pi }{4}[/tex] which means that you would be dividing the 2π by 8 ([tex]\frac{2\pi }{8} =\frac{\pi }{4}[/tex] )
The shift is always added at the end of the function.
- For vertical shifts, the shift is added separately as it's own individual value. (A good example would be the last option in your sc; [tex]y=6sin(8x)+\frac{\pi }{2}[/tex]).
- For horizontal shift, the shift is joined with the x in the parentheses. If you want to think about it this way, the horizontal axis is the x-axis. Therefore, it makes sense that if it's a horizontal shift, the shift will be with the x.
Using all this information, we can determine that the answer has to have a 6 in front of it, an 8 multiplied with the x, and a [tex]\frac{\pi }{2}[/tex] in parentheses with the x.
Your final answer should be the 3rd option, [tex]y=6sin(8(x-\frac{\pi }{2} ))[/tex]
Answer:
[tex]y=6sin(8(x-\frac{\pi }{2} ))[/tex]
