2nd Reflection

Discontinuity:

-When finding discontinuity of a fraction you factor the top and bottom and cancel if you can then set equal to 0. If it can't be factored anymore then set the bottom equal to zero.

Example:

f(x) = 1/x+7

x+7=0< x=-7
continuous at -7

-Solving for piecewise, if the x-values are equal it's a jump. If they are not and there is no equal to sign then it's removable.

Example:

f(x) = {-3x+9 x<1
{x+9 x>-3

-3(1)+9=6 -3+9=6
x=6 it is a jump

-For vertical asymptotes there are 3 possible limits. Infinity, negative infinity, or DNE.

You draw a number line to see what X is approaching from the left and right. If both sides approach negative infinity or infinity then the limit is what you got, if the two sides approach different things then the limit does not exist.