What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2?

Question

michele_laino · Answer

hint:
the amplitude of your function is 2, since we have:
$$ - 2 \leqslant 2\cos \left( {\pi x} \right) \leqslant 2$$

michele_laino · Answer

the requested function is like below:
$$y = A\cos \left( {\frac{\pi }{k}} \right) + h$$
where A is the amplitude, h is the vertical shift, and k is such taht the period of that function is:
$$T = \frac{{2\pi }}{k}$$

michele_laino · Answer

that is the general formula, for your exercise

vera_ewing · Answer

So it's going to have to start out as f(x)= 3cos right?

michele_laino · Answer

yes!

vera_ewing · Answer

And the last part of the equation will be +2?

michele_laino · Answer

yes!

michele_laino · Answer

oops.. I have made a typo, here is the right formula:
$$y = A\cos \left( {\frac{x}{k}} \right) + h$$

vera_ewing · Answer

f(x) = 3 cos 2x + 2 ?

michele_laino · Answer

yes! that's right!

vera_ewing · Answer

Thank you, Michele! :)

michele_laino · Answer

thanks! :)