College Algebra MA1
College Algebra MA1 MAT 121
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This 2 page Class Notes was uploaded by Stephanie Batz on Monday October 12, 2015. The Class Notes belongs to MAT 121 at Front Range Community College taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/221864/mat-121-front-range-community-college in Math at Front Range Community College.
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Date Created: 10/12/15
MAT 121 College Algebra Review of graphing rational functions De nition fx where pX and qX are polynomials qX 0 Note px is 106 qx reduced Tools for graphing 1 Find the intercepts a X intercepts Set pX 0 and solve ie set numerator to zero and solve or fX 0 b y intercepts Find f0 ie X 0 2 Find the veltical asymptotes Set qX 0 and solve X a X b etc ie VA occur when f is in reduced form and the denominator is zero f gtiooaSX gtaetc A function will never cross its vertical asymptotes 3 Find the horizontal asymptotes Let the degree of polynomial pX numerator be n with leading coef cient a Let the degree of polynomial qX denominator be m with leading coef cient b a y 0 n lt m Degree of num less that the degree ofthe denom b y ab n m Degree of num equal to degree ofthe denom c No HA n gt m Degree of num greater than the degree of the denom Determine the value of f as X approaches positive or negative in nity ie HA occur when the yvalues approach a number when X approaches in nity f gt b as X gt i 00 A function can cross its horizontal asymptote 4 Find any slant asymptotes When the degree of pX numerator is eXactly one more than the degree of qX denominator then f has a slant asymptote y aX b Found by dividing qX into pX using long division and ignoring any remainder 5 Find any symmetry a Even function fX fX implies yaXis symmetry b Odd function fX fX implies origin symmetry 6 Find eXtra points Use the table feature in ASK mode on the independent variable on the calculator to nd speci c points 7 Note once all Xintercepts have been found and plotted on the coordinate plane the graph will not cross the XaXis at any other point