Describe how the graph of y= abs(x-2) is related to the parent graph?
My answer: The graph is shifted 2 units to the right (or in the positive direction) in comparison to the parent graph.
if by the parent graph you mean y = │x│, then correct.
To understand how the graph of y = |x - 2| is related to the parent graph, we need to examine the effect of each part of the equation.
First, let's consider the parent graph, y = |x|. This is the absolute value function, which is a V-shaped graph symmetric about the y-axis. It passes through the origin (0, 0) and extends upward and downward along the y-axis.
Now, let's focus on the equation y = |x - 2|. The subtraction inside the absolute value function, (x - 2), indicates a shift of the graph horizontally by 2 units to the right. This means that the entire graph of |x| is shifted 2 units in the positive x-direction. The vertex, where the V-shape of the absolute value graph changes direction, will now occur at x = 2.
So, compared to the parent graph, the graph of y = |x - 2| is simply a horizontal shift of 2 units to the right.