Honors Pre-Calc- Unit Two

Removable Discontinuity

There is a whole in the graph that can be "plugged"

Non-removable Discontinuity

There is a vertical asymptote that breaks up the graph

Non-removable Jump Discontinuity

Often a piece-wise function

Bounded Below

When a number is less than or equal to every other point on the graph

Bounded Above

When a number is greater than or equal to every other point on the graph

Bounded

The function is bounded above and below

Absolute Extrema

The highest or lowest point on the graph

Local Extrema

A high or low point on the graph(compared the points around it)

Even Function

When negative and positive x equal y.
f(x)=f(-x)

Odd Function

When negative x equal negative y. When positive x equal positive y.
f(-x)=-f(x)

(fog)(x)

Replace the x in g(x) with f(x)

(gof)(x)

Replace the x in f(x) with g(x)

Inverse Functions

Functions f and g are inverses only if (fog)(x)=(gof)(x)=x

End Behavior Model(m=n)

y=a/b

End Behavior Model(m>n)

No asymptote

End Behavior Model(m<n)

y=0

Domain Restricts(Square root)

If there are no negatives in the square root then set the radicand greater than or equal to zero

Domain Restricts(Fractions)

If there are no zeros in the denominator than set the denominator not equal to zero

Domain Restricts(Logs)

If there are no zeros and negatives inside of the log than set the a value greater than 0

One-to-one

When the function and it's inverse are functions