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# PCExam 1 study guide answers

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### PCExam 1 study guide answers

1. 1. Precalculus<br />Exam 1 Study Guide<br />Be able to provide two examples for each of the following:<br /><ul><li>Natural numbers (positive whole numbers)
2. 2. Integers (whole numbers)
3. 3. Rational numbers (ratio of two integers)
4. 4. Real numbers (any number that is not imaginary)
5. 5. Pure imaginary numbers (any number that is a multiple of i=-1)
6. 6. Complex numbers (has a real and an imaginary part)</li></ul>Composition of functions:<br />Let fx=2+2x and gx=3x2. Find:<br />1.fgx=2+6x2 <br />2.gfx=6+6x<br />3.ffx=2+22+2x<br />4.ggx=27x4<br />Let fx=-7+8x2+g(x) and gx=2x+1. Find:<br />1.fg1=72<br />2.gf-3=-5<br />3.ff2=7254<br />4.gg-1=-1<br />Find the inverse of each function. Verify each inverse by composition.<br />1.fx=2+4xf-1x=x2-24<br />2.gx=32-xg-1x=-x3+2<br />3.hx=7x-14h-1x=4x+17<br />4.fx=-1+8x3f-1x=3x+18<br />For each set of complex numbers:<br />(a) plot on a complex plane<br />(b) find the modulus of both<br />(c) find the distance between the two numbers<br />(d) find the midpoint between<br />(e) add them<br />(f) subtract the second from the first<br />(g) multiply them<br />(h) divide the first by the second using conjugates.<br /> 1.3-2i2.3+2i<br />-4-6i4-i<br />(1.b)3-2i=13(2.b)3+2i=13<br />-4-6i=524-i=17<br />(1.c)65(2.c)10<br />(1.d)-12-4i(2.d)72-12i<br />(1.e)-1-8i(2.e)7+i<br />(1.f)7+4i(2.f)-1+3i<br />(1.g)-24-10i(2.g)14+5i<br />(1.h)i2(2.h)10+11i17<br />3.1+7i4.5-i<br />-2-i5+i<br />(3.b)1+7i=8(4.b)5-i=26<br />-2-i=55+i=26<br />(3.c)4.721(4.c)2<br />(3.d)-12+7-12i(4.d)5<br />(3.e)-2+7-27+1i(4.e)26<br />(3.f)-2-7+-27+1i5(4.f)24-10i26<br />For each function:<br />(a) graph on the coordinate plane (show any asymptotes with a dashed line)<br />(b) classify (constant, linear, quadratic, cubic, even polynomial, odd polynomial, piecewise, absolute value, radical, rational, exponential or logarithmic)<br />(c) state domain and range<br />1.y=-3x+2(b) linear(c) dom: R, ran: R<br />2.y=x-12+2(b) quadratic, even polynomial(c) dom: R, ran: 2,∞ or {y∈R|y≥2}<br />3.y=4(b) constant(c) dom: R, ran: {4}<br />4.y=3x+1(b) radical (cube root)(c) dom: R, ran: R<br />5.y=x-5(b) absolute value(c) dom: R, ran: [0,∞) or {y∈R|y≥0}<br />6.y=x3-2(b) cubic, odd polynomial(c) dom: R, ran: R<br />7.y=ex(b) exponential(c) dom: R, ran: (0,∞) or {y∈R|y>0}<br />8.y=ln(x+1)(b) logarithmic(c) dom: (0,∞) or {x∈R|x>0}, ran: R<br />9.y=x2+2x+1(x+1)(b) rational(c) dom: (-∞,-1)∪(-1,∞) or {x∈R|x≠-1}, ran: R<br />10.y=x2-3x+4x2-1(b) rational(c) dom: (-∞,-1)∪(-1,1)∪(1,∞) or {x∈R|x≠±1}<br />11.y=3, x<12x+1, 1≤x≤5-5, x>5(b) piecewise(c) dom: R, ran: -5∪[3,11] or {y∈R|y=-5 or 3≥y≥11}<br />Find the limit.<br />1.limx->-1x2+2x+1x+1=0<br />2.limx->1x2-3x+4x2-1=DNE<br />3.limx->∞2x2-3x+4x2-1=2<br />4.limx->-∞1x=0<br />5.limx->∞x3+4x+1x2+x-1=∞<br />