transform function f(x)=x^2 into a new function g(x) by shifting f(x)horizontally 9units to the rig t, reflecting the result across the x axis, and then shifting the result up 4 units. find the equation g(x)
f(x) = -(x-9)^2 +4
The -9 does the horizontal shift. The minus sign does the reflection about the x axis and the +4 does the upward shift.
To transform the function f(x) = x^2 into the new function g(x) by shifting it horizontally 9 units to the right, reflecting it across the x-axis, and then shifting the result up 4 units, you can follow these steps:
Step 1: Start with the function f(x) = x^2
Step 2: Shift f(x) horizontally 9 units to the right:
To shift a function horizontally, you replace x with (x - h), where h represents the horizontal shift. In this case, h = 9 since we want to shift 9 units to the right.
So, f(x) = (x - 9)^2
Step 3: Reflect the function across the x-axis:
To reflect a function across the x-axis, you need to change the sign of the function. In this case, the negative sign will be outside the function.
Therefore, f(x) = -(x - 9)^2
Step 4: Shift the result up 4 units:
To shift a function vertically, you add a constant term outside the function. In this case, 4 units up will be represented by +4 outside the function.
Thus, g(x) = -(x - 9)^2 + 4
So, the equation for the new function g(x) is g(x) = -(x - 9)^2 + 4.