Question

The graph of f(x) = x2 was transformed to create the graph of g(x) = (x − 7.5)2. Which of these describes this transformation?

A.
A horizontal shift to the right 7.5 units

B.
A horizontal shift to the left 7.5 units

C.
A vertical shift down 56.25 units

D.
A vertical shift up 56.25 units

Answer 1

The graph of g(x) = (x - 7.5)^2 is derived from the graph of f(x) = x^2 by shifting it horizontally to the right by 7.5 units.

Step-by-step explanation:

The transformation described from the graph of f(x) = x^2 to g(x) = (x - 7.5)^2 involves a change in the horizontal position of the graph. When we compare the two functions, we can see that g(x) is derived from f(x) by replacing x with (x - 7.5). This operation means for g(x) to have the same value as f(x), x must be 7.5 units larger. Therefore, this translates to a horizontal shift to the right by 7.5 units for the entire graph of f(x) to obtain the graph of g(x).

Answer 2

A. A horizontal shift to the right 7.5 units

Step-by-step explanation:

Replacing x with x-7.5 shifts the graph 7.5 units to the right.

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In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.