Question

For some real number c, the graph of the function y = |x – 20|+| x + 18| and y = x
+ c intersect at exactly one point. Number of possible integral values of c.
​

Answer 1

Given : y = |x – 20|+| x + 18|

y = x + c

intersect at exactly one point.

To Find : Number of possible integral values of c.

​Solution:

y = |x – 20| +| x + 18|

case 1 :

x ≥  20

=> y = x - 20 + x  + 18

=> y = 2x - 2

  y  = x + c

=> 2x - 2  = x + c

=> x =  c +  2

x ≥ 20

=> c  ≥  18

x ≤ - 18

=> y = 20 - x  + x + 18

=> y = 38

=> y = x + c

=> 38 = x + c

x ≤ - 18

=> c ≥ 56

-18 < x < 20

=> y = |x – 20| +| x + 18|

=> y = 20 - x + x + 18

=> y = 38

y = x + c

=> 38 = x + c

=> c =  38 - x

-18 < x < 20

=>   18   <  c  < 56

  c  ≥  18

  c ≥ 56

 18   <  c  < 56

intersect at exactly one point hence

c = 18  

Number of possible integral values of c is  1

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