Question

Question is: Which equation represents the graph?

A. y= |x|-2
B. y=|2x|-2
C. y=|x-2|
D. y=|2x-2|

Please show work

Answer 1

B. y = |2x| - 2.

Explanation:

If we start with y = 2x:

this passes through the origin and has a slope of 2.

y = |2x| means the absolute ( positive) values only, so the part of the line below the x axis is reflected in the axis to form a V shaped graph.

So we have a V shaped graph with the vertex at (0, 0).

Then -2 brings the vertex from (0, 0) to (0 -2) so we get:

y = |2x| - 2.

Answer 2

Based on the image, the correct equation is C. y = |x - 2|.

Here's why:

Absolute value function: The graph shows a V-shaped pattern centered around x = 2, which is characteristic of the absolute value function.

Symmetry: The graph is symmetrical around the vertical line x = 2. This means the absolute distance from the line is the same for both positive and negative values of x.

This eliminates options A and B, as they are not symmetrical.

Shift: The graph is shifted two units down compared to the basic absolute value function (y = |x|).

This shift corresponds to the -2 in option C.

Therefore, considering the V-shape, symmetry, and shift, y = |x - 2| accurately represents the graph in the image.