Question

12. Draw the graph of y =|x - 1|+|x - 3|

Answer 1

Answer:

Drawing the graph of a function containing multiple modulus functions is easy if you know how to plot y=|x| .

Shifting this graph one unit to the left gives you the graph of y=|x+1| .

If you shift the graph to the right by one unit instead, you’ll get the graph of y=|x−1| .

Add all the three graphs shown above.

This is the graph of y=|x+1|+|x|+|x−1| .

Here’s a more analytical solution. The graph of |x| changes direction at x=0 , so we must look at the piecewise definitions of |x+1|+|x|+|x−1| between intervals marked off by {−1,0,1} .

y=|x+1|+|x|+|x−1|

⟹y=⎧⎩⎨⎪⎪⎪⎪−3x2−xx+23xx<−1−1≤x<00≤x<1x≥1

Draw the graphs of all four of these on the same paper. You’ll end up with a graph that looks like the one shown above.

Step-by-step explanation:

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Answer 2

Answer:

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