Review the basic features of sinusoidal functions: midline, amplitude, and period.

What are midline, amplitude, and period?

Midline, amplitude, and period are three features of sinusoidal graphs.
start color maroonC, M, i, d, l, i, n, e, end color maroonC is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.
start color greenD, A, m, p, l, i, t, u, d, e, end color greenD is the vertical distance between the midline and one of the extremum points.
start color purpleC, P, e, r, i, o, d, end color purpleC is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).
Want to learn more about midline, amplitude, and period? Check out this video.

Finding features from graph

Given the graph of a sinusoidal function, we can analyze it to find the midline, amplitude, and period. Consider, for example, the following graph.
It has a maximum point at left parenthesis, 1, comma, 7, right parenthesis, then a minimum point at left parenthesis, 3, comma, 3, right parenthesis, then another maximum point at left parenthesis, 5, comma, 7, right parenthesis.
The horizontal line that passes exactly between y, equals, 7 (the maximum value) and y, equals, 3 (the minimum value) is start color maroonC, y, equals, 5, end color maroonC, so that's the midline.
The vertical distance between the midline and any of the extremum points is start color greenD, 2, end color greenD, so that's the amplitude.
The distance between the two consecutive maximum points is start color purpleC, 4, end color purpleC, so that's the period.
Problem 1
What is the midline equation?
y, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Want to try more problems like this? Check out these exercises: