Chapter 3, Problem 35SGA

To determine

To find: Whether $y=x^2+2;x=2$ is continuous at the given x-value. Justify your response using the continuity test.

Answer to Problem 35SGA

Yes

Explanation of Solution

Given information: $y=x^2+2;x=2$

Calculation:

  $y=x^2+2\text{ is }$ a polynomial.

All polynomials are continuous by definition.

However, using the continuity test, because as x approaches 2 from the left and right,

The function approaches 6. And

  $f\left(2\right)=6$

Then the function is defined at x = 2.