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How do you graph #y < |2x + 3|#?

Answer 1

Isaiah Anthony

When #(2x+3) < 0#
#y< abs(2x+3) "implies " y " is below the line " y = -2x-3#

For ease of drawing the graph, note that #y=-2x-3# has intercepts at #(0,-3) " and " (-3/2,0)#

When #(2x+3) >= 0#
#y< abs(2x+3) "implies " y " is below the line " y = 2x+3#

Again, for ease of drawing the graph, note that #y=2x+3# has intercepts at #(0,+3) " and "(-3/2,0)#

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Answer 2

Savannah Anderson

To graph the inequality y < |2x + 3|, you first graph the boundary line y = |2x + 3|, then shade the region below the boundary line.

Graph the boundary line y = |2x + 3| by considering two cases: a. When 2x + 3 ≥ 0: y = 2x + 3 b. When 2x + 3 < 0: y = -(2x + 3)
Shade the region below the boundary line to represent y < |2x + 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.

How do you graph #y &lt; |2x + 3|#?

How do you graph #y < |2x + 3|#?