Rewrite functions in equivalent forms to reveal and explain useful properties.
Normalize a sine or cosine equation and read features
Problem
Normalize \(y~=~3\sin(2x)~+~4\). State \(A\), \(B\), \(h\), and \(D\); give the amplitude and reflection, period and quarter-period, phase shift, midline, and range.
Big Picture
What this problem is really about
Normalize the entire angle into the form with an inside coefficient multiplying a shifted input before reading any horizontal feature. Then assign the parameters by role: the outside coefficient gives amplitude and reflection, the inside coefficient gives period, the horizontal parameter gives phase shift, and the outside constant gives the midline. Use midline plus and minus amplitude to confirm the range.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
