Question

Is the function given by ​g(x)equals= left brace Start 2 By 2 Matrix 1st Row 1st Column one third x plus 5 comma 2nd Column for x less than 6 comma 2nd Row 1st Column negative x plus 13 comma 2nd Column for x greater than 6 comma EndMatrix 1 3x+5, for x<6, −x+13, for x>6, continuous at xequals=66​? Why or why​ not?

Answer 1

Answer:

  No. g(6) is undefined.

Step-by-step explanation:

A function is continuous when the left limit is equal to the right limit at a point, and the function is defined as the limit value at that point.

This function is not defined at x=6, so cannot be continuous there. (Also, the limit values from the different directions are different.)