1. In each of the following, transformations are applied to the graph of $y=f(x)$ when indicated replacements are made. In each case
- Describe which transformations are applied to the graph when the indicated replacements are made
- Determine the equation of the final graph if the replacements are made in the order given
a) Replace $x$ with $x+2$ and $y$ with $-y$
b) Replace $x$ with $4 \mathrm{x}$ and $y$ with $y-7$
c) Replace $x$ with $\frac{1}{3} x, y$ with $-2 y$, and $y$ with $y+2$
d) Replace $x$ with $2 x, y$ with $\frac{1}{4} y, x$ with $-x$ and $y$ with $y+10$

Step 1 ：The problem is asking for the transformations applied to the graph of a function when certain replacements are made. It also asks for the equation of the final graph after these replacements.

Step 2 ：For part a), replacing \(x\) with \(x+2\) corresponds to a horizontal shift of the graph 2 units to the left. Replacing \(y\) with \(-y\) corresponds to a reflection of the graph in the x-axis.

Step 3 ：The final equation of the graph can be obtained by making these replacements in the original equation \(y=f(x)\).

Step 4 ：Assuming the original function is a linear function \(y = mx + c\), we can substitute \(x\) with \(x+2\) and \(y\) with \(-y\) in the equation to get the final equation.

Step 5 ：The final equation of the graph after the replacements is \(y = -mx - 2m - c\). This equation represents a line that has been shifted 2 units to the left and reflected in the x-axis.

Step 6 ：\(\boxed{\text{Final Answer: The transformations applied to the graph are a horizontal shift of 2 units to the left and a reflection in the x-axis. The equation of the final graph is } y = -mx - 2m - c}\)