Question

Describe how g(x) is a transformation of f(x) = x2 if a. g(x) = x2 + 3 b. g(x) = (x - 2)2 c. g(x) = x2 - 1 d. g(x) = (x + 4)2

Answer 1

For the first, you know that

`\begin{gathered} \text{If} \\ y=f\mleft(x\mright)+c \\ \text{You shift the graph of y=f(x) up by c units} \end{gathered}`

So, g(x)=x^(2) +3 will be to move f (x) = x^(2) 3 units up, to move f (x) = x^(2) 3 units up, as can you see in the graph.

Therefore, the graph of f (x) is shifted 3 units up.

`\begin{gathered} \text{ If} \\ y=f(x-c) \\ \text{ you shift the graph of y=f(x) to the right c units} \\ \end{gathered}`