What will happen to the given function if a graph is shifted 2 units left and 3 units up?(2 points) f(x)=x^3 will become g(x)= ( x+?)^3 +?

Question

GPT-4o mini · Answer

To shift the graph of the function $ f(x) = x^3 $ 2 units to the left and 3 units up, we need to adjust the function accordingly. 1. **Shifting left by 2 units:** To shift a function to the left by $ h $ units, we replace $ x $ with $ x + h $. Here, $ h = 2 $, so we replace $ x $ with $ x + 2 $: $$ f(x) = (x + 2)^3 $$ 2. **Shifting up by 3 units:** To shift a function up by $ k $ units, we add $ k $ to the entire function. Here, $ k = 3 $, so we add 3 to the function: $$ g(x) = (x + 2)^3 + 3 $$ Putting it all together, the function $ g(x) $ becomes: $$ g(x) = (x + 2)^3 + 3 $$ Thus, in the form $ g(x) = (x + ?)^3 + ? $, we have: - The first question mark (for the left shift) is **2**. - The second question mark (for the upward shift) is **3**. Final answer: $$ g(x) = (x + 2)^3 + 3 $$ (where $ ? = 2 $ and $ ? = 3 $).