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How do you graph # y = 2 | x - 1 | - 3#?

Answer 1

graph{y=2|x-1|-3 [-10, 10, -5, 5]}

A standard absolute value graph looks like this: graph{y=|x| [-10, 10, -5, 5]} This graph was translated 1 unit right and 3 units down. (you know this because the equation includes #|x-1|# and #-3#) From the 2 in front of the equation, you know the graph was dilated by a factor of 2, giving you your final answer.

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Answer 2

Avery Alexander

To graph ( y = 2 | x - 1 | - 3 ), follow these steps:

Plot the vertex at (1, -3).
Use the slope of 2 to plot additional points. From the vertex, move one unit to the right and two units up to plot another point. Then, move one unit to the left and two units up to plot another point.
Draw a smooth curve through the plotted points to represent the graph of ( y = 2 | x - 1 | - 3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.