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Prac_Final - M 305G Name Practice for Final 1 Graph at...

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M 305G Practice for Final Name: 1. Graph at least two cycles for each of the following functions. Label a few points and any asymptotes. (a) f ( x ) = tan( x 4 ) (b) h ( x ) = 3 sec( πx ) Page 1 of 9
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M 305G Practice for Final 2. Let R ( x ) = x 2 - x - 2 x 2 - 2 x - 8 = ( x - 2)( x +1) ( x - 4)( x +2) (a) Find the y -intercept and x -intercept(s) of R ( x ). (b) Find the horizontal or oblique asymptote of R ( x ). Find any points where the graph of R ( x ) crosses this asymptote. (c) Find the vertical asymptote(s) of R ( x ). (d) Graph y = R ( x ), clearly labeling each feature from parts (a)-(c). Page 2 of 9
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M 305G Practice for Final 3. Decide if the following functions are even, odd, or neither. Show your work (guessing gets zero points). (a) f ( x ) = 2 x x +3 (b) g ( x ) = x 3 x 2 +1 (c) h ( x ) = x 2 + cos( x ) 4. Evaluate the following trigonometric functions. (a) tan 4 π 3 · = (b) sin 5 π 6 + 4 π · = (c) sec - 2 π 3 · = Page 3 of 9
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M 305G Practice for Final 5. Find the inverses of the following functions. (a) g ( x ) = 3 e 2 x +1 - 1 (b) h ( x ) = 6 + 7 ln( x + 8) (c) f ( x ) = 2 tan(3 x ) 6. Find the oblique asymptote of the function R ( x ) = 2 x 2 - x +2 x - 1 Page 4 of 9
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