Describe how the graphs of y = absolute x and y = absolute x +2 are related.

http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx+%2B2%7C

To understand the relation between the graphs of y = |x| and y = |x| + 2, we first need to examine the individual equations.

The graph of y = |x| represents the absolute value function, which essentially means that the output (y) will always be positive or zero, regardless of the input (x). This function produces a "V" shape, symmetric with respect to the y-axis. For x > 0, the graph steadily increases as x increases, and for x < 0, it steadily decreases as x decreases. The vertex, where the graph changes direction, is at the origin (0, 0) in this case.

Now, let's consider the equation y = |x| + 2. Compared to the previous equation, we have added a constant value of 2 to the output. This means that the entire graph will shift upwards by 2 units.

In other words, the graph of y = |x| + 2 will have the same overall "V" shape, but it will be shifted vertically upwards by 2 units. The vertex, which was previously at the origin (0, 0), will now be at (0, 2).

To better understand this relationship, you can also plot the graphs on a coordinate plane using software like graphing calculators or online graphing tools. By comparing the two graphs side by side, you can visually observe the shift. Additionally, plugging in different x-values into the equations can help you compare the corresponding y-values and see the impact of the constant term.

By understanding the general properties of the absolute value function and how adding a constant affects a graph, you can easily describe the relationship between y = |x| and y = |x| + 2.