Question

Is this continuous or not continuous everywhere?

y=x^2-9/x^2-5x+6

Answer 1

hint: x^2 - 9 factors to (x-3)(x+3)

x^2 - 5x + 6 factors to (x-3)(x-2)

Answer 2

okay so you would then cancel the x-3 on top and bottom

Answer 3

yes, so the expression simplifies to

(x+3)/(x-2)

Answer 4

keep in mind that because (x-3)(x-2) is in the denominator, this means that

(x-3)(x-2) = 0

turns into

x = 3 or x = 2

so if either x = 3 or x = 2, then you have division by zero errors, which means the function isn't continuous at these points

Answer 5

ohh that makes sense, thank you sooo much!

Answer 6

sure thing