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Active Prelude to Calculus

Preview Activity 2.4.1.
Let \(f(t) = \cos(t)\text{.}\) First, answer all of the questions below without using Desmos; then use Desmos to confirm your conjectures. For each prompt, describe the graphs of \(g\) and \(h\) as transformations of \(f\) and, in addition, state the amplitude, midline, and period of both \(g\) and \(h\text{.}\)
(a)
\(g(t) = 3\cos(t)\) and \(h(t) = -\frac{1}{4}\cos(t)\)
(b)
\(g(t) = \cos(t-\pi)\) and \(h(t) = \cos\left(t+ \frac{\pi}{2}\right)\)
(c)
\(g(t) = \cos(t)+4\) and \(h(t) = \cos\left(t\right)-2\)
(d)
\(g(t) = 3\cos(t-\pi)+4\) and \(h(t) = -\frac{1}{4}\cos\left(t+ \frac{\pi}{2}\right)-2\)