Questions: Let f(x) = sqrt(x). Find g(x), the function that is f(x) shifted up 4 units and left 8 units. g(x) =

Solution Steps

To find the function \( g(x) \) that represents \( f(x) = \sqrt{x} \) shifted up 4 units and left 8 units, we need to apply transformations to \( f(x) \). Shifting a function up by 4 units involves adding 4 to the function, and shifting it left by 8 units involves replacing \( x \) with \( x + 8 \). Therefore, the transformed function \( g(x) \) is given by \( g(x) = \sqrt{x + 8} + 4 \).

The original function is defined as: \[ f(x) = \sqrt{x} \]

To find the function \( g(x) \) that represents \( f(x) \) shifted up 4 units and left 8 units, we perform the following transformations:

1. Shift Left by 8 Units: Replace \( x \) with \( x + 8 \).
2. Shift Up by 4 Units: Add 4 to the function.

Thus, the transformed function \( g(x) \) is given by: \[ g(x) = \sqrt{x + 8} + 4 \]

Final Answer