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

<span>The graph will shift 5 units to the right and 1 unit upwards, forming a parabola that opens up with its vertex positioned at (5, 1).

Explanation:
The subtraction of 5 from x prior to squaring indicates a horizontal movement of 5 units to the right.

The addition of 1 signifies a vertical shift of 1 unit up.

This transformation follows the vertex form of a parabola, y=a(x-h)^2 + k, where (h, k) represents the vertex. In this case, h is 5 and k is 1, placing the vertex at (5, 1).</span>

Answer:

The function f(x) has been shifted 5 units to the right and moved 1 unit upward to create g(x) as shown below.

Step-by-step explanation:

We know that,

The function has been moved to form the function .

Thus, we see that,

The f(x) function has been translated 5 units to the right which results in the function .

Moreover, this function is then elevated by 1 unit creating the function g(x).

In summary, the function f(x) is translated 5 units to the right and 1 unit upwards leading to g(x).

Consequently, the graph of g(x) appears as follows.