The graph of g(x) is the graph of f(x)=x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)?
Please explain how to do it and not just give me the answer :-)

Question

The graph of g(x) is the graph of f(x)=x^2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)? 
Please explain how to do it and not just give me the answer :-)

aum · Answer

$f(x) = x^2$
f(x+4) shifts f(x) to the LEFT by 4 units.  
$f(x+4) = (x+4)^2$
$k * f(x)$ stretches f(x) vertically by a factor of k.
Therefore, $3 \times f(x+4) = 3(x+4)^2$
f(x) + C  shifts f(x) vertically up by C units.
Therefore, $3 \times f(x+4) + 5 = 3(x+4)^2 + 5 = g(x)$  or 
$g(x) = 3(x+4)^2 + 5 $