Find the value of the constant 𝑐 that makes the following function continuous on (−∞,∞) .

Question

f(y)={ cy+8 if y ∈ (-oo,6]

cy^2-8 if y ∈ (6,oo)

C=

Answer 1

The pieces cy+8 and cy^2-8 are polynomials. They are continuous everywhere. To make f(y) continuous, the pieces must come together at 6:

c6+8 = c6^2-8

8+8 = c6^2-c6

16 =c(30)

c=16/30 = 8/15