4x What is the function g(x) created from f(x)=x^2 by moving the graph left 2 units, vertically stretchi 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

To determine the function $g(x)$ created from $f(x)=x^{2}$ by moving the graph left 2 units and vertically stretching it, we need to apply the given transformations to the original function.<br /><br />Step 1: Moving the graph left 2 units<br />When a graph is moved left or right, it means that the x-coordinate of each point on the graph is shifted. In this case, the graph is moved left 2 units, which means that the x-coordinate of each point will be decreased by 2. Therefore, the new function after moving the graph left 2 units is:<br />$g(x) = (x+2)^{2}$<br /><br />Step 2: Vertically stretching the graph<br />Vertical stretching means that the y-coordinate of each point on the graph is multiplied by a certain factor. In this case, the factor is 3. Therefore, the new function after vertically stretching the graph is:<br />$g(x) = 3(x+2)^{2}$<br /><br />Therefore, the correct answer is C: $g(x)=3(x+2)^{2}+5$.