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# Class Note for MATH 1330 at UH

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COURSE
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Class Notes
PAGES
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KARMA
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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 25 views.

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Date Created: 02/06/15
Slant asymptote The graph of the function may have a slant asymptote if the degree of the numerator is greater than the degree of the denominator To nd the equation of the slant asymptote use long division to divide the denominator into the numerator The quotient is the equation of the slant asymptote Behavior near the vertical asymptotes The graph of the function will approach either Do or Do on each side of the vertical asymptotes To determine if the function values are positive or negative in each region nd the sign of a test value close to each side of the vertical asymptotes Crossing points The graph of the function may cross the horizontal asymptote You may be asked to nd the crossing point To nd it set the function equation to horizontal asymptote and solve for x This will give you the x coordinate of the crossing point To nd the y coordinate substitute in the value you found for the x coordinate Example 1 Find all of the features of f x i1 and use them the graph the function x Math 1330 Class Notes 7 Section 23 Page 2 of7 x3 Example 2 Find all of the features of f x and use them to graph the function no he 5 dommm x22 10 Y L bb13917dc l 07 E 39 39 39 quot x 1Mquot 344420 szg LMM39 LHD 1 Hq x ato Math 1330 Class Notes 7 Section 23 Page 3 of7 2x2 8 Example 3 Find all of the features of fx 2 2 and use them to graph the x function O owm m Xv39JJCscDio if X112 x111 if w0ugu2w HQ 1333 jxiz 39Xrl MoiC at 39 TL 2 4 xo L 1531 3 H 23 1 1 319139 39 X wt lbwth x 1 vi a 39 aha raw 44 5 4 Math 1330 Class Notes 7 Section 23 Page 4 of7 Example 4 Find all of the features of fx x function 2 x y l39xL VOx Ib L w 97449 1 7 1 Math 1330 Class Notes 7 Section 23 Page 5 of7 and use them to graph the Hs w a 2 domam x L i D x 1 7 L o01u21ao no MARS F39mH DVLWIXH 0 7c 117 m MM LUV Diff 0 7 VIA X D39ZO x19 S Ul39LXA39Q 3 2 Example 5 Find all of the features of fx and use them to x x graph the function i m 7quot H7 LY quot39 7quot m W L L W W Lac H IL 1 stiiitttit mmimwimm Lif EZZE D Ejl DCKMQ Ne m dmm v Lntwpio 0 X xvtlio KHz i0 x H ki l i tp Ht quotdaw ut s uqn Ei i g wquot 57 lek IW 1 77W 4231 Y1 3 V AP D 7Q k0 x x quot vx v lc NMW 1 1 2 Math 1330 Class Notes 7 Section 23 Page 6 of 7 x 2 X vllx x 4L4 lt39 745 2 4 7 91L C 1x2 4x rm W 7m 17 C V 0 591 33 s h 9 do 31 2 7 Example 6 Determine if fx 4x 3x 1 x2 3x 2 give the x coordinate of the crossing point 2 334 Ri e Ll ux LEM 341 1 441x ltz gX 397 fax 4 x73 crosses its horizontal asymptote If so X Example 7 Determine if f x crosses its horizontal asymptote If so give x2 3x 2 the x coordinate of the crossing point 143A v3 0 iv a z 3739l77xlcg quot O X igxig Mama ngr 0 6967 X23 X 1iKAh 21 x Math 1330 Class Notes 7 Section 23 Page 7 of7 A rational function is a function of the form f x 333 M XZVSyib CNN Math 1330 Section 23 Rational Functions Pot Where P and Q are polynomial QX functions and Qx 7t 0 You ll need to be able to nd the following features of the graph of a rational function and then use the information to sketch the graph Domain Intercepts Holes Vertical asymptotes Horizontal asymptote Slant asymptote Behavior near the vertical asymptotes Crossing points Domain The domain of f is all real numbers except those values for Which Qx 0 x intercepts The x intercepts of the function Will be all values of x for Which Px 0 but Qx 7t 0 y intercept The y intercept of the function is f 0 Holes The graph of the function Will have a hole at any value of x for Which both Px 0 and Qx 0 Vertical asymptotes The graph of the function has a vertical asymptote at any value of x for Which Qx 0 but Px 7t 0 Horizontal asymptote You can determine if the graph of the function has a horizontal asymptote by comparing the degree of the numerator With the degree of the denominator if the degree of the numerator is smaller than the degree of the denominator then the graph of the function has a horizontal asymptote at y 0 if the degree of the numerator is equal to the degree of the denominator then the graph of the function has a horizontal asymptote at 7 leading coef cent of numerator leading coef cient of denominator if the degree of the numerator is greater than the degree of the denominator then the graph of the function does not have a horizontal asymptote Math 1330 Class Notes 7 Section 23 Page 1 of7

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