Chapter Closure
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Period: π
Amplitude: 3
Period: π
Amplitude: no amplitude
y&= acos[ b(x- h)]+k [0.5em]
a&=amplitude
b&=period
h&=horizontal translation
k&=vertical translation
Examining the given equation, we see that the coefficient to cos(2x) is 3. This means it has an amplitude of 3. Also, the coefficient to x is 2, which means it has half the period. With this information, we can draw its graph.
The locator point is a point on the graph that is easily identifiable, such as (0,3).
Let's summarize what we have found. Period:& π Amplitude:& 3
y&= atan[ b(x- h)]+k [0.5em]
a&=stretch factor
b&=period
h&=horizontal translation
k&=vertical translation
As we can see, the tangent curve has no amplitude. It does have a horizontal shift of π2 to the right. With this information, we can draw its graph.
The locator point is a point on the graph that is easily identifiable, such as ( π2,0).
Let's summarize what we have found. Period:& π Amplitude:& no amplitude