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PCExam 1 practice with answers


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PCExam 1 practice with answers

  1. 1. Precalculus<br />Practice Exam 1 (100 points)<br />1.Give 2 examples for each set of numbers. (12 points)<br />Pure ImaginaryRealRationalIntegerNatural079375ComplexComplex<br />2.Choose one of the following problems, either (a) or (b). (6 points)<br />If fx=9x2+1 and gx=x-1, find<br />a)fgxb)gfx<br />3.Choose one of the following problems, either (a) or (b). (6 points)<br />If fx=2x2+1 and gx=3x2+x, find<br />a)ff-4b)gg2<br />4.Choose one of the following, either (a) or (b). (6 points)<br />Find the inverse of the function.<br />a)fx=4x2-13b)gx=2x+1<br />5.Verify by composition the inverse from #4. (6 points)<br />6.For ONE of the following sets of complex numbers, (14 points)<br />a) plot the numbers on the complex plane<br />b) find the moduli of both numbers<br />c) find the distance OR the midpoint between the numbers<br />d) add the numbers<br />e) subtract the numbers<br />f) multiply the numbers<br />g) divide the numbers using conjugates<br />for bonus:<br />6+2i1+i2+3i<br />-4+i-1-i1+i<br />7-10.Choose FOUR of the following functions. (8 points each)<br />a) Classify (constant, linear, quadratic, cubic, even polynomial, odd polynomial, piecewise, absolute value, radical, rational, exponential, or logarithmic)<br />b) Graph, showing any asymptotes with a dashed line<br />c) State domain and range<br />y=x2-x-2x-1 y=x-1+2y=x+23-1<br />y=x+2x+2x-1y=x-4<br />11.Choose THREE of the following limits to evaluate. (6 points each)<br />a)limx->-1x2+2x+1x+1<br />b)limx->1x2-3x+4x2-1<br />c)limx->∞2x2-3x+4x2-1<br />d)limx->-∞1x<br />e)limx->∞x3+4x+1x2+x-1<br />Answers:<br />2.<br />a)fgx=9x-12+1=9x-9+1=9x-8<br />b)gfx=9x2+1-1=9x2=3x<br />3.<br />a)ff-4=2-42+1=216+1=32+1=33<br />b)gg2=322+2=34+2=12+2=14<br />4.<br />a)f-1x=3x+14<br />b)g-1x=x2-12<br />5.<br />a)ff-1x=43x+142-13=43x+14-13=3x+1-13=3x3=x<br />b)gg-1x=2x2-12+1=x2-1+1=x2=x<br />6.6+2i and -4+i<br />b)6+2i=40 and -4+i=17<br />c)distance: 101, midpoint: 1+12i<br />d)2+3ie)10+if)-26-2ig)-22-14i17<br />1+i and -1-i<br />b)1+i=2 and -1-i=2<br />c)distance: 2, midpoint: 0<br />d)0e)2+2if)-2ig)-1<br />2+3i and 1+i<br />b)2+3i=7 and 1+i=2<br />c)distance: 1+0.73≈0.856, midpoint: 32+3+12i≈1.5+1.37i<br />d)3+3+1ie)1+3-1if)2-3+2+3ig)2+3+-2+3i2 <br />7-10.<br />y=x2-x-2x-1 <br />a)rational<br />b)hole at x=1, graph y=x+2<br />c)domain: xx≠1, range: R<br />y=x-1+2<br />a)radical<br />b)graph of y=x shifted up 2 and right 1<br />c)domain: {x|x≥1}, range: {y|y≥2}<br />y=x+23-1 <br />a)cubic, odd polynomial<br />b)graph of y=x3, shifted down 1 and left 2<br />c)domain: R, range: R<br />y=x+2x+2x-1<br />a)rational<br />b)hole at x=-2, vertical asymptote at x=1, horizontal asymptote at y=0<br />d)domain: {x|x≠-2,x≠1}, range: {y|y≠0}<br />y=x-4<br />a)absolute value<br />b)graph of y=x, shifted right 4<br />c)domain: R, range: {y|y≥0}<br />