**Problem Statement: Graph Transformation** Given: Let \( f(x) = 4\sqrt{x} \). **Task:** If \( g(x) \) is the graph of \( f(x) \) shifted down 6 units and left 1 unit, write a formula for \( g(x) \). **Solution:** - The transformation of a function \( f(x) \) by shifting it horizontally to the left by \( h \) units is given by \( f(x + h) \). - Vertically shifting the graph down by \( k \) units is achieved by subtracting \( k \) from the function, resulting in \( f(x) - k \). **Applying the transformations:** 1. Shift left by 1 unit: Replace \( x \) with \( x + 1 \) in \( f(x) \). \[ f(x+1) = 4\sqrt{x+1} \] 2. Shift down by 6 units: Subtract 6 from the function. \[ g(x) = 4\sqrt{x+1} - 6 \] Thus, the formula for \( g(x) \) is: \[ g(x) = 4\sqrt{x+1} - 6 \] **Instructions:** - Enter \( \sqrt{x} \) as `sqrt(x)`. - For further assistance, select "Message instructor." - [Submit Question Button]

Given that, the graph of the function is $f\left(x\right)=4\sqrt{x}$ and also given that, the function shifted down 6 units and left 1 unit.

"Vertical Shifts:

If c is a positive real number, the graph of  $f\left(x\right)+c$ the graph of $y=f\left(x\right)$ shifted upward c units.

 If c is a positive real number, the graph of  $f\left(x\right)-c$ the graph of $y=f\left(x\right)$ shifted downward c units.

Horizontal Shift:

If c is a positive real number, then the graph of  $f\left(x-c\right)$ is  the graph of $y=f\left(x\right)$ shifted to the right c units.

If c is a positive real number, then the graph of  $f\left(x+c\right)$ is  the graph of $y=f\left(x\right)$ shifted to the left c units.."