Activity 1.8.2.
(a)
On the same axes as the plot of \(y = r(x)\text{,}\) sketch the following graphs: \(y = g(x) = r(x) + 2\text{,}\) \(y = h(x) = r(x+1)\text{,}\) and \(y = f(x) = r(x+1) + 2\text{.}\) Be sure to label the point on each of \(g\text{,}\) \(h\text{,}\) and \(f\) that corresponds to \((-2,-1)\) on the original graph of \(r\text{.}\) In addition, write one sentence to explain the overall transformations that have resulted in \(g\text{,}\) \(h\text{,}\) and \(f\text{.}\)
(b)
On the same axes as the plot of \(y = s(x)\text{,}\) sketch the following graphs: \(y = k(x) = s(x) - 1\text{,}\) \(y = j(x) = s(x-2)\text{,}\) and \(y = m(x) = s(x-2) - 1\text{.}\) Be sure to label the point on each of \(k\text{,}\) \(j\text{,}\) and \(m\) that corresponds to \((-2,-3)\) on the original graph of \(s\text{.}\) In addition, write one sentence to explain the overall transformations that have resulted in \(k\text{,}\) \(j\text{,}\) and \(m\text{.}\)
(c)
Now consider the function \(q(x) = x^2\text{.}\) Determine a formula for the function that is given by \(p(x) = q(x+3) - 4\text{.}\) How is \(p\) a transformation of \(q\text{?}\)
