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) = x
2 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.
To understand this, we can look at the vertical & horizontal translations of a parabola of the form
A vertically translated parabola has the form , where k is the vertical shift upward when k is positive and vertical shift downward when k is negative.
A horizontally translated parabola has the form , where a is the horizontal shift rightward when a is positive and horizontal shift leftward when a is negative.
When we replace x of the original function with (x-1), we have . According to the rules, this means that the original function is shifted 1 unit right (horizontal shift).
The statement that is true is very obvious it will be that d will intersect the point at which the statement will obviously be d because the rest make no sense
, where k is the vertical shift upward when k is positive and vertical shift downward when k is negative.
, where a is the horizontal shift rightward when a is positive and horizontal shift leftward when a is negative.
