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 g(x) = (x – 5)2 + 1 represents the translation of the graph of f(x) = x2. It is a parabola shifted 5 units to the right and 1 unit upward.

Step-by-step explanation:

The graph of g(x) = (x – 5)2 + 1 represents the translation of the graph of f(x) = x2. When we translate a graph horizontally by adding or subtracting a constant value inside the function, the graph shifts left or right. In this case, the graph of f(x) is shifted 5 units to the right to form the graph of g(x). The +1 at the end of the function shifts the graph vertically upward by 1 unit. So, the correct graph would be a parabola shaped like the graph of f(x), but shifted 5 units to the right and 1 unit upward.

Answer 2

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.