Question

what is period, amplitude, and range of y=7+3sin2(x-2.5)

Answer 1

Hey Michelle,
\(\Large\bf \color{#CC0033}{\text{Welcome to OpenStudy! :)}}\)

Answer 2

So here is the general form,
\[\Large\sf y=\color{orangered}{a}\sin \color{#3366CF}{b}(x-\color{#CC0033}{c})+\color{#A57F02 }{d}\]

\(\Large\sf\color{orangered}{a}\) gives us the amplitude,
\(\Large\sf 2\pi/\color{#3366CF}{b}\) gives us the period,
\(\Large\sf \color{#CC0033}{c}\) is a horizontal shift to the right,
and \(\Large\sf \color{#A57F02}{d}\) is a vertical shift upward.

Applying this to our problem,\[\Large\sf y=\color{orangered}{3}\sin \color{#3366CF}{2}(x-\color{#CC0033}{2.5})+\color{#A57F02 }{7}\]

Answer 3

Oh we also need to deal with the range right? Hmm let's see.

Answer 4

Normally sine goes up to 1, and down to -1.
That's when it starts at zero and has an amplitude of 1.

So for our problem we instead start at 7,
and our amplitude tells us we can go up 3 from there and down 3 from there.

So our function has a range from 4 to 10.
Does that make sense? :o

Answer 5

yess it does thank you. i never understood that you needed to put the 7 after everything else :) thanks a lot!!