Question

current skill $ write the expression that completes the equation to represent the result of transforming y = |x| with the steps listed below. 1: reflect the function across the x-axis. 2: shift the function 1 unit to the right. y =

Explanation:

Step1: Reflect across x - axis

To reflect a function \( y = f(x) \) across the \( x \) - axis, we use the transformation \( y=-f(x) \). For the function \( y = |x| \), after reflecting across the \( x \) - axis, the function becomes \( y=-|x| \).

Step2: Shift 1 unit right

To shift a function \( y = f(x) \) \( h \) units to the right, we use the transformation \( y = f(x - h) \). Here, \( h = 1 \) and the function after reflection is \( y=-|x| \), so after shifting 1 unit to the right, we replace \( x \) with \( x - 1 \). The function becomes \( y=-|x - 1| \).

Answer:

\( y=-|x - 1| \)