Question

The graph below represents the function f(x) and the translated function g(x) .

If f(x) = x ^ 2 , which of the following functions could be an algebraic representation of g(x) ?

Answer 1

Answer:  D.  $g(x) = (x-b)^2$

Explanation:

If we want to shift the curve some distance b to the right, then we'll need to replace x with x-b. What this effectively does is shift the xy axis itself b units to the left while the curve is fixed in place. This gives the illusion of the curve moving b units to the right.

Put another way: the old input x is updated to the new input x-b which is smaller by b units. This helps explain why the xy axis is shifted to the left this amount.

So that's how we go from $f(x) = x^2$ to $g(x) = (x-b)^2$. You can think of it as $g(x) = f(x-b) = (x-b)^2$