PCExam 1 study guide answers
- 1. Precalculus<br />Exam 1 Study Guide<br />Be able to provide two examples for each of the following:<br />Natural numbers (positive whole numbers)
- 3. Rational numbers (ratio of two integers)
- 4. Real numbers (any number that is not imaginary)
- 5. Pure imaginary numbers (any number that is a multiple of i=-1)
- 6. Complex numbers (has a real and an imaginary part)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 />