Find numbers $k$, so that $f$ is continuous at every point.
14)
\[
f(x)=\left\{\begin{array}{ll}
9 x+9, & \text { if } x< -3 \\
k x+10, & \text { if } x \geq-3
\end{array}\right.
\]

Step 1 ：For a function to be continuous at a point, the limit of the function as x approaches that point from the left (negative side) must be equal to the limit of the function as x approaches that point from the right (positive side).

Step 2 ：In this case, we need to find the value of k such that the function is continuous at x = -3.

Step 3 ：This means we need to set the two parts of the function equal to each other at x = -3 and solve for k.

Step 4 ：The equation for the left side of the function at x = -3 is \(9x + 9\), which simplifies to -18.

Step 5 ：The equation for the right side of the function at x = -3 is \(kx + 10\), which simplifies to \(10 - 3k\).

Step 6 ：Setting these two equations equal to each other gives us the equation \(-18 = 10 - 3k\).

Step 7 ：Solving this equation for k gives us \(k = \frac{28}{3}\).

Step 8 ：Final Answer: The value of k that makes the function continuous at every point is \(\boxed{\frac{28}{3}}\).