The graph of g(x) is the graph of f(x)=x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule of g(x)?
can someone explain how to get the correct answer? how do i solve this?
step one is xnew = x+4 to shift left y = (x+4)^2 so zero at x = -4
step two is y' = 3 y to multiply function by three y = 3(x+4)^2
step three more up 5, y = 5 + 3(x+4)^2
so g(x) = 3 (x+4)^2 + 5
You are welcome.
Thank you so much!!
To find the function rule of g(x) given the transformations applied to f(x), you can follow these steps:
1. Start with the original function f(x) = x^2.
2. Shift 4 units left: To shift the graph 4 units to the left, subtract 4 from x. This gives us f(x + 4) = (x + 4)^2.
3. Vertically stretch by a factor of 3: Multiply the whole function by 3. This gives us 3 * f(x + 4) = 3 * (x + 4)^2.
4. Shift 5 units up: Add 5 to the function. This gives us g(x) = 3 * (x + 4)^2 + 5.
Therefore, the function rule of g(x) is g(x) = 3 * (x + 4)^2 + 5.