Question

Continuity question:

Answer 1

Let f(x) = \begin{cases} m x - 16, &\text{if}\ x< -9\\ x^2+8 x - 7, &\text{if}\ x\geq -9 \end{cases}
If f(x) is a function which is continuous everywhere, then we must have
m=

Answer 2

To be continuous the functions must be equal at the switchover from one form to another, at the -9 value. So the two functions will be equal when x=-9, plug it in and find m.

Answer 3

Should it be like this: m(-9)-16=(-9)^2+8(-9)-7?

Answer 4

Yes, that is it. Well done!

Answer 5

So what is m?

Answer 6

m= -2