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

Choice A is correct.

Explanation:

We have given that

f(x) = x²

We have to find the description of the graph f(x-1).

f(x-1) = (x-1)²

When we replace x with x-a , the resulting graph is a horizontal shift of f(x) by a units to the right.

The graph of f(x-1) is horizontal shift of f(x) by 1 units to the right.

Hence, Choice A is correct.

Answer 2

A

Explanation:

To understand this, we can look at the vertical & horizontal translations of a parabola of the form
`f(x)=x^2`

• A vertically translated parabola has the form
  `f(x)=x^2+k`, 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
  `f(x)=(x-a)^2`, 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
`f(x)=(x-1)^2`. According to the rules, this means that the original function is shifted 1 unit right (horizontal shift).

Correct answer is A.