Question

Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right?

a- f(x) = x[ + 1
b-f(x) = |x-1|
c- f(x) = |-*[ + 1
d- fx) = |-x-11

Answer 1

The absolute value function that represents f(x) = |x| reflected over the x-axis and translated 1 unit to the right is f(x) = -|x-1|.

Step-by-step explanation:

To find the absolute value function that represents the parent function f(x) = |x|, reflected over the x-axis and translated 1 unit to the right, we need to apply two transformations to the parent function. Reflecting a function over the x-axis is achieved by multiplying the function by -1, and translating a function 1 unit to the right is obtained by substituting x with (x-1). Therefore, the transformed function is f(x) = -|x-1|. This function is the reflection of |x| over the x-axis because of the negative sign in front of the absolute value, which reflects all y-values, and it is translated 1 unit to the right because the inside of the absolute value is (x-1), meaning every x-value is effectively increased by 1.