Question

Describe the transformation of 2|x-1|-2?

(a) f(x) is a vertical stretch of g(x) by a factor of 2.
(b) f(x) is a horizontal shift of g(x) to the right by 1 unit.
(c) f(x) is a reflection of g(x) across the y-axis.
(d) f(x) is a vertical shift of g(x) down by 2 units.

Answer 1

The transformation 2|x-1|-2 includes a horizontal shift to the right by 1 unit, a vertical stretch by a factor of 2, and a vertical shift down by 2 units.

Step-by-step explanation:

The transformation of the function 2|x-1|-2 involves several steps. First, consider the absolute value function, denoted by |x|. The transformation |x-1| shifts this function horizontally to the right by one unit, which corresponds to the function |x-d| where d is the distance shifted to the right.

Next, the function is affected by a vertical stretch by a factor of 2, which is seen in the expression 2|x-1|. This means the vertical size of the graph is increased by a factor of two, making the peaks and valleys of the graph twice as high from the x-axis compared to the basic |x| function.

The last transformation is a vertical shift downward by two units, which is represented by the '-2' at the end of the function. Graphically, this means the entire graph is moved down by two units along the y-axis.

Therefore, the transformed function 2|x-1|-2 includes the following transformations: