High School

Find all values \( x = a \) where the function is discontinuous.

\[
f(x) =
\begin{cases}
3 & \text{if } x < 6 \\
x + 6 & \text{if } 6 \leq x \leq 9 \\
15 & \text{if } x > 9
\end{cases}
\]

Answer :

Final answer:

The function is discontinuous at x = 6 and x = 9.

Explanation:

The function is discontinuous at values of x = 6 and x = 9. To find these values, we need to determine where the function changes its behavior. We see that for x < 6, the function is defined as 3. At x = 6, the function changes to x + 6, and at x = 9, the function changes again to 15. Therefore, the values of x = 6 and x = 9 are where the function is discontinuous.

The function is discontinuous at values of x = 6 and x = 9.

When x < 6, the function is defined as 3.

When 6 ≤ x ≤ 9, the function is defined as x + 6.

When x > 9, the function is defined as 15.

Therefore, at x = 6, there is a jump in the function from 3 to 6 + 6 = 12, making it discontinuous. Similarly, at x = 9, there is another jump from 9 + 6 = 15 to 15. Hence, those are the values of x where the function is discontinuous.

Learn more about Discontinuity here:

https://brainly.com/question/33663012

#SPJ11