Question

the functions using horizontal and vertical shifts. Compare f(x) =x^(2) and f(x-1)=(x-1)2 using tables if x values are 1,2,3, and 4. How many units did the function shift and in whigh direction? -2 and to the left O-1 and to the right Tand to the right

Answer 1

The function f(x-1) = (x-1)^2 shifted the function f(x) = x^2 one unit to the right.

Step-by-step explanation:

To compare the functions f(x) = x^2 and f(x-1) = (x-1)^2 using tables, we can plug in the given x-values and observe how the y-values change.

For f(x) = x^2, when x = 1, the function gives us y = 1^2 = 1. When x = 2, y = 2^2 = 4. When x = 3, y = 3^2 = 9. And when x = 4, y = 4^2 = 16.

For f(x-1) = (x-1)^2, when x = 1, the function gives us y = (1-1)^2 = 0. When x = 2, y = (2-1)^2 = 1. When x = 3, y = (3-1)^2 = 4. And when x = 4, y = (4-1)^2 = 9.

Comparing the two tables, we can see that the function f(x-1) = (x-1)^2 shifted the original function f(x) = x^2 one unit to the right. The function f(x) = x^2 represents a parabola centered at the origin, while f(x-1) = (x-1)^2 represents a parabola centered at (1, 0).