Help with continuity of functions

[Cacophony]

Homework Statement

For each of the following functions, find a value of a, (if such a value exists), which makes the function continuous.

a) f(x) = {ax^2...x > 3
...{x - 7...x ≤ 3

b) f(x) = {sin(ax)...x < (pi)
...{1...x ≥ (pi)

c) f(x) = {x^2 + a^2...x > 1
...{9 - x....x ≤ 1

Does anyone know how to do these?

 

[tiny-tim]

Hi Cacophony!

for (a), the only difficulty is at x = 3 …

so put the two equations equal at x = 3 ​

 

[HallsofIvy]

Do you know the definition of "continuous"? That's a good place to start.