If you're good at math, please help: Find the constants a and b such that the function is continuous on the entire real line.

Answers:

a = -2

b = -1

Explanation:

The first piece 5 must match up with the ax+b when x = -2, or else the function wouldn't be continuous at this junction.

Plug in x = -2 and set the result equal to 5

We end up with -2a+b = 5

Solving for b gets us b = 5+2a

The middle piece ax+b must also equal the third piece -5 when x = 3 to ensure the second junction is continuous.

This leads us to the equation 3a+b = -5

Apply substitution and solve for 'a'

3a+b = -5

3a+5+2a = -5

5a+5 = -5

5a = -5-5

5a = -10

a = -10/5

a = -2 is one of the answers

Then use this to find b

b = 5+2a

b = 5+2(-2)

b = 5-4

b = -1 is the other answer