Graph y=|x|

Problem

y=|x|

Solution

1. Identify the parent function as the absolute value function, which is defined piecewise as y=x for x≥0 and y=−x for x<0

2. Determine the vertex of the graph by finding where the expression inside the absolute value is zero, which occurs at (0,0)

3. Calculate points to the right of the vertex by choosing positive values for x such as (1,1) and (2,2)

4. Calculate points to the left of the vertex by choosing negative values for x such as (−1,1) and (−2,2)

5. Plot the points and connect them to form a V-shaped graph that is symmetric about the y-axis.

Final Answer

The graph of y=|x| is a V-shaped curve with its vertex at the origin (0,0) and sides following the lines y=x and y=−x

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