Determine whether the function is continuous or discontinuous at xr=1. Examine the

three conditions in the definition of continuity.

fx2+8 if x<1

f (x)

= 6x2 - 3 if x> 1

Answer:

1. f (x) is continuous at x = 1

2. f (x) is continuous at x = 1

Step-by-step explanation:

Determine whether the function is continuous or discontinuous at x=1.

Examine the three conditions in the definition of continuity.

1. f (x) = x²+8 if x<1

2. f (x) = 6x² - 3 if x> 1

For a function to be continuous at a given x-value

then lim x→a f (x) = f (a)

Meaning that

What this is saying is that, as x gets closer to a, f (x) should also get closer to f (a).

1. Limit of f (x) = x² + 8 at x = 1

= 1²+8 = 9

f (a) = f (1) = 1² + 8 = 9.

lim x→a f (x) = f (a) = 9

2. Limit of f (x) = 6x² - 3 at x = 1

= 6 (1²) - 3 = 3

f (a) = f (1) = 6 (1²) - 3 = 3

lim x→a f (x) = f (a) = 3