Question

find all if any points of discontinuity of h(x) write answers as coordinate points.
h(x)= (x^2 -4x -5)/(x^2 -25)

Answer 1

discontinuity means that x cannot take on certain values.

Answer 2

in this case, the denominator cannot be 0.

Answer 3

Points of discontinuity are places where the graph is undefined. So, you can find it just by setting the denominator to 0.

Answer 4

solve x^2-25=0

Answer 5

would there be one at 5 and -5?

Answer 6

Use the identity\[a^{2} - b^{2} = (a - b)(a + b)\]

Answer 7

Yes, x = 5 and x = -5.

Answer 8

ok i was kinda confused because i thought it was just when the same thing crossed out of the numerator and denominator, but its just when the denominator = 0?

Answer 9

somethings the numerator also contains discontinuities

Answer 10

sometimes*

Answer 11

But since the numerator is a normal quadratic equation, you do not need to concern it yet