Limits and continuity. Please help.

Question

anonymous · Answer

To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

anonymous · Answer

$$f(x)=\left[\begin{matrix}3x+k, & x \le -4 \ kx^2 -5, & x > -4\end{matrix}\right]$$

anonymous · Answer

It's not a matrix, but a function with conditions I didn't know how to make that.

anonymous · Answer

I know the basics of limits, but this one caught me off guard.

anonymous · Answer

For the function to be continuous everywhere, it must be continuous at x=4. Therefore both conditions bust be equal at x=4 ie: $$3x+k=kx^{2}-5$$ at x=4

From there plug in a known x and solve for k.

anonymous · Answer

So, plug in x = 4? or something arbitrarily close to it?

anonymous · Answer

Or rather, -4

anonymous · Answer

I got -0.47 ish, and that's one of the answers. Thanks!