Question

If f(x) = x2, which of the following describes the graph of f(x - 1)? A. The graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the right. B. The graph of f(x - 1) is a vertical shift of f(x) = x2 one unit down. C. The graph of f(x - 1) is a vertical shift of f(x) = x2 one unit up. D. The graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the left.

Answer 1

The answer is (A) the graph of f(x - 1) is a horizontal shift of f(x) = x² one unit to the right

Explanation:

∵ f(x) = x² is represented by parabola its vertex is (0 , 0)

∵ f(x -1) = (x - 1)² = x² - 2x + 1

∴ The x-coordinate of its vertex = -(-2)/2(1) = 1 ⇒ (-b/2a)

∴ The y-coordinate of it = (1 - 1)² = 0

∴ The vertex point is (1 , 0)

∴ The graph moves horizontally 1 unit to the right