Question

Determine the value of the constant a for which the function f(x) is continuous at -3. x2 +5x +6 if x#-3 f(x)x+3 if x3 The function f(x) is continuous at -3 when a _____

a) A = - 3
b) A=-2
c) A =2
d) A =0
e)A= 1
f)A = -1

Answer 1

The value of the constant a for which the function f(x) is continuous at -3 is -1 (option f) A = -1).

Step-by-step explanation:

To determine the value of the constant a for which the function f(x) is continuous at -3, we need to compare the left-hand and right-hand limits of the function at x = -3.

The left-hand limit is given by x² + 5x + 6 and the right-hand limit is given by x + 3. Since f(x) is continuous at x = -3, the left-hand and right-hand limits must be equal. Therefore, the value of a is -1 (option f) A = -1).