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How does the graph of y=∣3∣ compare to the graph of y=∣x−2∣?

A. Both have the same slope.
B. Both have the same y-intercept.
C. Both have the same x-intercept.
D. They are identical.

User Antsyawn
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1 Answer

6 votes

Final answer:

The graph of y=|3| is a horizontal line at y=3 with no slope, while the graph of y=|x-2| is V-shaped with a x-intercept at (2, 0), so they have different characteristics and are not identical. The correct answer is B.

Step-by-step explanation:

The question asks how the graph of y=|3| compares to the graph of y=|x-2|. The first equation, y=|3|, represents a horizontal line at the value of 3 on the y-axis since the absolute value of 3 is always 3, regardless of the value of x.

On the other hand, the equation y=|x-2| represents a V-shaped graph. This graph has two different slopes depending on whether x is greater than or less than 2. The point when x is exactly 2 is where the graph intersects the x-axis, so the x-intercept is at (2, 0).

y=|3| does not have an x-intercept; it's always above the x-axis. Meanwhile, y=|x-2| does not maintain the same y-value. Therefore, the correct answer is B, both graphs have different y-intercepts, the graph of y=|3| intersects the y-axis at 3, and the graph of y=|x-2| has a y-intercept at (0, 2).

User Dan Malcolm
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