You are told that the function $$g\left(x\right)$$ is the result of shifting the graph of $$f\left(x\right)=x^2$$ up 7 units and then vertically stretching it by a factor of 3. What is the rule for $$g\left(x\right)$$ ?

You are told that the function $$g\left(x\right)$$ is the result of shifting the graph of $$f\left(x\right)=\left|x\right|$$ right 5 units and then horizontally stretching it by a factor of 4. What is the rule for $$g\left(x\right)$$ ?

The graph of $$f\left(x\right)=\left|x\right|$$ is vertically compressed by a factor of 1/2, compressed horizontally by a factor of 1/3, and then shifted up 6 units and left 9 units to arrive at the graph of $$g\left(x\right)$$ . What is the rule for $$g\left(x\right)$$ ?