1. Aaron Thomas Jacob Wefel Tyler Sneen

3.  By the end of this lesson we will introduce the terminology that is used to describe functions  These include: Domain, Range, Continuity, Discontinuity, upper and lower bound, Local and absolute maximums and minimums, and asymptotes

4.  The domain of a function is all of the possible x-values the function can have. It can be expressed as an inequality  The Range of a function is all of the possible y-values the function can have. It is also expressed as an inequality

5.  Domain: All Real Numbers  Range: All Real Numbers  Domain: x> -1  Range: x>-5

6.  A graph has continuity if its graph is connected to itself throughout infinity. There are no asymptotes or holes in the graph  A Graph has removable discontinuity if its graph has a hole where one x value was removed from the domain  A graph has infinite discontinuity if its graph has an asymptote that can not be replaced with only one value

7. Jump Discontinuity Removable Discontinuity

8.  A function is bounded above or below if the graph’s range doesn’t extend past a certain point above or below.  A function is “Bounded” if the function’s range doesn’t extend below or above certain points  If the function has no restrictions on its range’s extent the function is considered “unbounded”

9.  This sine function is bounded above and below at 1 and -1

10.  A Local Maximum/Minimum of a function is the highest/lowest point of the range in the surrounding window of the graph  The absolute maximum/minimum of a function is the highest/lowest point of the entire range of the graph

11.  Local Min: 3, -4, 4  Local Max: 5  Absolute Max: None (Graph goes infinitely upward)  Absolute Min: -4

12.  A horizontal asymptote is a part of the function which gets infinitely close to a Y- value but never touches it  A Vertical asymptote is a part of the function which gets infinitely close to a x- value but never touches it

13.  Identify any horizontal or vertical asymptotes of the graph of  You would first start by foiling the denominator… = (x+1)(x-2)  This means that the graph has vertical asymptotes of x=-1 and x=2  Because the denominator’s power is bigger than the numerator’s, y = 0 no matter what the value of x is  Now you have x/((x+1)(x-2)) = 0  This means that the horizontal asymptote is zero