4x What is the function g(x) created from f(x)=x^2 by moving the graph left 2 units, vertically stretching it by a factor of 3, and shifting the graph up - unitis? A g(x)=2(x+3)^2+5 B g(x)=3(x-2)^2+5 C g(x)=3(x+2)^2+5 D g(x)=5(x+3)^2+2

## Step 1<br />The problem involves the transformation of the function \(f(x) = x^{2}\). The transformations are:<br />- Moving the graph left 2 units<br />- Vertically stretching it by a factor of 3<br />- Shifting the graph up 5 units<br /><br />## Step 2<br />The transformations can be represented as follows:<br />- Moving the graph left 2 units is represented by \(x+2\)<br />- Vertically stretching it by a factor of 3 is represented by multiplying the function by 3<br />- Shifting the graph up 5 units is represented by adding 5 to the function<br /><br />## Step 3<br />Combining these transformations, we get the function \(g(x) = 3(x+2)^{2}+5\).