Determine the values of a and b that make f(x) continuous.
D) No values of a and b will make f(x) continuous.

Question

Determine the values of a and b that make f(x) continuous. 
D) No values of a and b will make f(x) continuous.

Quizplus · Accepted Answer

For f(x) to be continuous, the limit of f(x) as x approaches 2 from both the left and right sides must be equal to f(2).

Thus, we need to solve for the value of a and b such that:

lim x→2- [a(x-2) + b] = lim x→2+ [3x-4]
a(2-2) + b = 3(2) - 4
b = 2

lim x→2- [a(x-2) + b] = lim x→2+ [3x-4]
a(2-2) + 2 = 3(2) - 4
a = 1

Therefore, the values of a = 1 and b = 2 will make f(x) continuous. The correct choice is C.

Determine the Values of a and B That Make F(x)