Question

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.Which graph represents g(x)?

Answer 1

The graph of $f(x)=x^2$ and the graph of $g(x)=(x-5)^2+1$. These two graphs are illustrated in the Figure bellow. So, let's explain what this means:

• For a function f(x), a new function g(x) = f(x - c) represents to shift the graph c units to the right.
• For a function f(x), a new function g(x) = f(x) + k represents to shift the graph k units upward.

Since in our problem the function g(x) = f(x - c) + k, we have shifted the function f(x) c units to the right and k units upward, that is, we have shifted the function f(x) 5 units to the right and 1 unit upward as indicated in the Figure bellow.

Answer 2

Answer:

Option A on edge