Question

Is the function h(x) = (x² - 9) / (x + 3) continuous at x = 3?
1) True
2) False

Answer 1

The function h(x) = (x² - 9) / (x + 3) is continuous at x = 3.

Step-by-step explanation:

To determine if the function h(x) = (x² - 9) / (x + 3) is continuous at x = 3, we need to check if the limit of the function exists at x = 3 and if it equals the value of the function at x = 3. Let's start by evaluating the limit.

lim[h(x)] as x approaches 3 = lim[(x² - 9) / (x + 3)] as x approaches 3.

We can directly substitute x = 3 into the function:

h(3) = (3² - 9) / (3 + 3) = 0.

By substituting x = 3 and simplifying, we find that h(3) equals 0. Thus, the function is continuous at x = 3. So the correct answer is 1) True.