Activity 1.8.3.
(a)
On the same axes as the plot of \(y = r(x)\text{,}\) sketch the following graphs: \(y = g(x) = 3r(x)\) and \(y = h(x) = \frac{1}{3}r(x)\text{.}\) Be sure to label the point on \(g\) and \(h\) that corresponds to the point \((-2,-1)\) on the original graph of \(r\text{.}\) In addition, write one sentence to explain the overall transformations that have resulted in \(g\) and \(h\) from \(r\text{.}\)
(b)
On the same axes as the plot of \(y = s(x)\text{,}\) sketch the following graphs: \(y = k(x) = -s(x)\) and \(y = j(x) = -\frac{1}{2}s(x)\text{.}\) Be sure to label the point on \(k\) and \(j\) that corresponds to the point \((-2,-3)\) on the original graph of \(s\text{.}\) In addition, write one sentence to explain the overall transformations that have resulted in \(k\) and \(j\) from \(s\text{.}\)
(c)
On the additional copies of the two figures below, sketch the graphs of the following transformed functions: \(y = m(x) = 2r(x+1)-1\) (at left) and \(y = n(x) = \frac{1}{2}s(x-2)+2\text{.}\) As above, be sure to label a key point on each graph that corresonds to the labeled point on the original parent function.
(d)
Describe in words how the function \(y = m(x) = 2r(x+1)-1\) is the result of three elementary transformations of \(y = r(x)\text{.}\) Does the order in which these transformations occur matter? Why or why not?
