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).