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