1. This practice exam covers topics like complex numbers, functions, limits, and graphing. 2. It asks students to choose problems involving adding, multiplying, composing, and finding inverses of various functions like f(x)=9x^2+1 and g(x)=x-1. 3. Students also must graph and classify functions, evaluate limits, and perform operations on complex numbers, plotting them on a plane. The exam covers concepts in precalculus.

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 />