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Describe how the graph of y= IxI – 7 is like the graph of y = IxI and how it is different.

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Answer:

Explanation:

The graph of y = |x| - 7 is similar to the graph of y = |x| in that both are V-shaped graphs that represent the absolute value function. However, there is a key difference between them:

**Similarity**:

- Both graphs have a V-shape that opens upward, which is characteristic of absolute value functions.

- They both have a vertex at the point (0, -7), where the graph intersects the y-axis. This is because, when x = 0, |x| = 0, and 0 - 7 = -7.

**Difference**:

- The graph of y = |x| is a V-shaped graph that intersects the x-axis at (0, 0) and doesn't have a vertical shift (shifting up or down).

- In contrast, the graph of y = |x| - 7 is the same as y = |x|, but it has been shifted downward by 7 units. This means that every point on the graph of y = |x| - 7 is 7 units below the corresponding point on the graph of y = |x|.

In summary, the key difference is the vertical shift downward by 7 units in the graph of y = |x| - 7 compared to y = |x|.

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