Reflection

In calculus this week our class learned how to find discontinuity, discuss continuity, properties of continuities, and finding vertical asymptotes.

When fidning a discontinuity, there are certain steps to solving if it is a fraction. When it's a fraction you factor the top and bottom, then concel if possible, then set equal to 0.
For Example:
f(x) = 3/x-2
It cannot factor anymore than it already is so set the bottom equal to zero.
x-2=0
x=2
So, it is not removable and continuous at x=2

While solving for piecewise function, you must see if the x-values are equal and if they are equal it's a jump; if not and there is no "-" then it's removable.
For Example:
f(x) = {-2x+3, x<1
{x^2, x > or = to 1
-2(1)+3=1
1^2=1
x=1 it is a jump.

When solving for vertical asymptotes, there are 3 possible limits which can be found: infinity, negative infinity, or does not exist (DNE).
For Example:
f(x) = 1/x-4
You draw a number line to see what 4 is approaching from the left which would be 3 and from the right 5.
So, the answer would be that 4 is approaching negative infinity from the left and positive infinity from the right.