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 :-)

Answer 1

\(f(x) = x^2\)
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
\(g(x) = 3(x+4)^2 + 5 \)