Question

Write the equation for an absolute value function that is shifted 4 units right, 1 unit up, and horizontally stretched by a factor of 2.

A) y = 2| x - 4 | + 1
B) y = | 2x - 8 | + 1
C) y = | x - 4 | + 2
D) y = | x - 2 | + 1

Answer 1

The equation of the absolute value function with the described transformations of shifting 4 units right, 1 unit up, and horizontal stretching by a factor of 2 is y = 2| x - 4 | + 1, which is option A.

Step-by-step explanation:

The student is asking for the equation of an absolute value function that incorporates a horizontal shift, a vertical shift, and a horizontal stretch. An absolute value function is generally given by f(x) = |x|, which can be modified with various transformations to move and stretch its graph.

To shift the graph 4 units to the right, we replace x with (x - 4). To shift the graph 1 unit up, we add 1 to the function, resulting in f(x) = |x - 4| + 1. A horizontal stretch by a factor of 2 is achieved by replacing x with x/2 inside the absolute value, which leads to f(x) = |(x/2) - 4| + 1. This simplifies to f(x) = 2| x - 4 | + 1, making option A the correct choice.