Question
What is the function g(x) created from f(x) = x^2 by moving the graph left 7 units, adding vertical compression by a factor of 1/6, and shifting the graph down 8 units?
Answers
GPT 3.5
To create the function g(x) from f(x) = x^2 by moving the graph left 7 units, adding vertical compression by a factor of 1/6, and shifting the graph down 8 units, we can apply these transformations in order.
1. Moving the graph left 7 units: Since moving the graph left 7 units involves changing the input variable x to x + 7, the function becomes f(x + 7) = (x + 7)^2.
2. Adding vertical compression by a factor of 1/6: Vertical compression involves stretching or shrinking the graph vertically. Shrink the graph by a factor of 1/6, we divide the function by 6, so the function becomes g(x) = (1/6)(x + 7)^2.
3. Shifting the graph down 8 units: Shifting the graph down 8 units involves subtracting 8 from the function, so the final function becomes g(x) = (1/6)(x + 7)^2 - 8.
Therefore, the function g(x) created from f(x) = x^2 by moving the graph left 7 units, adding vertical compression by a factor of 1/6, and shifting the graph down 8 units is g(x) = (1/6)(x + 7)^2 - 8.
1. Moving the graph left 7 units: Since moving the graph left 7 units involves changing the input variable x to x + 7, the function becomes f(x + 7) = (x + 7)^2.
2. Adding vertical compression by a factor of 1/6: Vertical compression involves stretching or shrinking the graph vertically. Shrink the graph by a factor of 1/6, we divide the function by 6, so the function becomes g(x) = (1/6)(x + 7)^2.
3. Shifting the graph down 8 units: Shifting the graph down 8 units involves subtracting 8 from the function, so the final function becomes g(x) = (1/6)(x + 7)^2 - 8.
Therefore, the function g(x) created from f(x) = x^2 by moving the graph left 7 units, adding vertical compression by a factor of 1/6, and shifting the graph down 8 units is g(x) = (1/6)(x + 7)^2 - 8.