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How do you graph #y=abs(x+2) +3#?

Answer 1

Avery Alexander

Set the absolute value function equal to 0:

#|x + 2| = 0#

#x + 2 = 0#

#x = -2#

This tells us that the minimum point occurs at #(-2,3)#

The right side graph has a slope of 1, therefore, we shall move 2 to the right of the minimum and plot the point #(0,5)#. Then we shall draw a ray from #(-2,3)# and through #(0,5)# toward infinity.

The left side graph has a slope of -1, therefore, we shall move 2 to the left of the minimum and plot the point #(-4,5)#. Then we shall draw a ray from #(-2,3)# and through #(-4,5)# toward infinity.

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Answer 2

Eva Adamson

To graph the equation ( y = |x + 2| + 3 ), you would first identify the vertex and the direction of the graph. The vertex is located at the point (-2, 3). Since the absolute value function always outputs non-negative values, the graph opens upwards from the vertex. You would then plot several points to the left and right of the vertex to sketch the graph of the absolute value function.

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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.