Write a formula for the function, $g(x)$, described as follows:
(3.00 Points) Use the function, $f(x)=x^{2}$. Move the function to the left by 1 unit and up by 5 units.
Answer
Final Answer: The transformed function is \(g(x) = \boxed{(x+1)^{2} + 5}\).
Step 1 ：The problem is asking for a transformation of the function \(f(x)=x^{2}\). The transformation involves moving the function to the left by 1 unit and up by 5 units.
Step 2 ：In terms of function transformations, moving a function to the left by 1 unit corresponds to replacing \(x\) with \((x+1)\) in the function.
Step 3 ：Moving a function up by 5 units corresponds to adding 5 to the function.
Step 4 ：Therefore, the transformed function, \(g(x)\), should be \(g(x) = (x+1)^{2} + 5\).
Step 5 ：Final Answer: The transformed function is \(g(x) = \boxed{(x+1)^{2} + 5}\).
