Question

Write an equation of an absolute value graph that has been vertically compressed by a factor of 1/2, reflected over the x-axis, translated down 2 units, and right 3 units.

A) y = -(1/2)|x - 3| - 2
B) y = (1/2)|x + 3| + 2
C) y = -(1/2)|x + 3| - 2
D) y = (1/2)|x - 3| + 2

Answer 1

The correct equation that represents the described transformations of an absolute value graph is y = -(1/2)|x - 3| - 2. This corresponds to the vertical compression, reflection, and translations as specified.

Step-by-step explanation:

The equation of an absolute value graph that has been vertically compressed by a factor of 1/2, reflected over the x-axis, translated down 2 units, and right 3 units is y = -(1/2)|x - 3| - 2.

To determine the correct transformations applied to the basic absolute value function f(x) = |x|, consider each transformation step-by-step:

• Vertical compression by a factor of 1/2 is achieved by multiplying the function by 1/2, resulting in f(x) = (1/2)|x|.
• Reflection over the x-axis is achieved by multiplying the function by negative one, giving f(x) = -(1/2)|x|.
• Translation down 2 units is denoted by subtracting 2 from the function, which results in f(x) = -(1/2)|x| - 2.
• Translation right 3 units shifts the variable x by adding 3 inside the absolute value, leading to the final equation y = -(1/2)|x - 3| - 2.

Considering the given options, the correct answer is A) y = -(1/2)|x - 3| - 2