How can the graph of $f(x)=\frac{1}{(x-4)^{2}}+14$ be obtained from the graph of $y=\frac{1}{x^{2}} ?$
A. By making a horizontal shift of 4 units to the right and a vertical shift of 14 units up
B. By making a horizontal shift of 4 units to the left and a vertical shift of 14 units down
C. By making a horizontal shift of 14 units to the right and a vertical shift of 4 units down
D. By making a horizontal shift of 14 units to the left and a vertical shift of 4 units up
Answer
Final Answer: \(\boxed{\text{A. By making a horizontal shift of 4 units to the right and a vertical shift of 14 units up}}\)
Step 1 ：The function $f(x)=\frac{1}{(x-4)^{2}}+14$ can be obtained from the function $y=\frac{1}{x^{2}}$ by shifting the graph of $y=\frac{1}{x^{2}}$ 4 units to the right and 14 units up. This is because the term $(x-4)^{2}$ in the denominator of $f(x)$ shifts the graph 4 units to the right, and the term +14 shifts the graph 14 units up.
Step 2 ：Therefore, the correct answer is A. By making a horizontal shift of 4 units to the right and a vertical shift of 14 units up.
Step 3 ：Final Answer: \(\boxed{\text{A. By making a horizontal shift of 4 units to the right and a vertical shift of 14 units up}}\)
