Which of the following is true for y=∣∣∣1−1|x|−2∣∣∣?
A
It has 2 asymptotes.
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B
It has 3 asymptotes.
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C
It is not differentiable at 5 points.
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D
It is not differentiable at 2 points.
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Solution
The correct options are B It has 3 asymptotes.
D It is not differentiable at 2 points. Follow the below steps to draw the graph of function y=∣∣∣1−1|x|−2∣∣∣
Step1: First draw the graph of function y=1x−2 Step 2: Now draw the graph for function y=1|x|−2 Step 3: Draw the graph of y=−1|x|−2 Step 4: Draw the graph of y=1−1|x|−2 Step 5: Now draw the graph of y=∣∣∣1−1|x|−2∣∣∣ From graph of step 5, it is clear that it has 3 asymptotes and not differentiable at 2 points.