1. In each of the following, transformations are applied to the graph of $y=f(x)$. In each case:
i) Describe IN WORDS which transformations are applied to the graph when the indicated replacements are made.
ii) Determine the equation of the final graph if the replacements are made in the order given.
a) Replace:
\[
x \rightarrow x+4
\]
\[
y \rightarrow 2 y
\]
\[
x \rightarrow-2 x
\]
b) Replace:
\[
\begin{array}{l}
x \rightarrow x-1 \\
y \rightarrow y-1
\end{array}
\]

Step 1 ：For part a), the replacements are: 1. \(x \rightarrow x+4\), 2. \(y \rightarrow 2y\), 3. \(x \rightarrow -2x\).

Step 2 ：The first replacement, \(x \rightarrow x+4\), is a horizontal shift of the graph 4 units to the left.

Step 3 ：The second replacement, \(y \rightarrow 2y\), is a vertical stretch of the graph by a factor of 2.

Step 4 ：The third replacement, \(x \rightarrow -2x\), is a horizontal reflection of the graph in the y-axis followed by a horizontal stretch by a factor of 2.

Step 5 ：Applying these transformations to a general function \(y=f(x)\) in the given order, we first replace \(x\) with \(x+4\) to get \(y=f(x+4)\).

Step 6 ：Then, replace \(y\) with \(2y\) to get \(2y=f(x+4)\).

Step 7 ：Finally, replace \(x\) with \(-2x\) to get \(2y=f(-2x+4)\).

Step 8 ：\(\boxed{2y=f(-2x+4)}\) is the equation of the final graph for part a).

Step 9 ：For part b), the replacements are: 1. \(x \rightarrow x-1\), 2. \(y \rightarrow y-1\).

Step 10 ：The first replacement, \(x \rightarrow x-1\), is a horizontal shift of the graph 1 unit to the right.

Step 11 ：The second replacement, \(y \rightarrow y-1\), is a vertical shift of the graph 1 unit down.

Step 12 ：Applying these transformations to a general function \(y=f(x)\) in the given order, we first replace \(x\) with \(x-1\) to get \(y=f(x-1)\).

Step 13 ：Then, replace \(y\) with \(y-1\) to get \(y-1=f(x-1)\).

Step 14 ：\(\boxed{y-1=f(x-1)}\) is the equation of the final graph for part b).