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PC Exam 1 study guide

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PC Exam 1 study guide

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
2. 2. Integers
3. 3. Rational numbers
4. 4. Real numbers
5. 5. Pure imaginary numbers
6. 6. Complex numbers</li></ul>Composition of functions:<br />Let fx=2+2x and gx=3x2. Find:<br />1.f(gx)<br />2.g(fx)<br />3.f(fx)<br />4.g(gx)<br />Let fx=-7+8x2+g(x) and gx=2x+1. Find:<br />1.f(g1)<br />2.g(f-3)<br />3.f(f2)<br />4.g(g-1)<br />Find the inverse of each function. Verify each inverse by composition.<br />1.fx=2+4x<br />2.gx=32-x<br />3.hx=7x-14<br />4.fx=-1+8x3<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 />3.1+7i4.5-i<br />-2-i5+i<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<br />2.y=x-12+2<br />3.y=4<br />4.y=3x+1<br />5.y=x-5<br />6.y=x3-2<br />7.y=ex<br />8.y=ln(x+1)<br />9.y=x2+2x+1(x+1)<br />10.y=x2-3x+4x2-1<br />11.y=3, x<12x+1, 1≤x≤5-5, x>5<br />Find the limit.<br />1.limx->-1x2+2x+1x+1<br />2.limx->1x2-3x+4x2-1<br />3.limx->∞2x2-3x+4x2-1<br />4.limx->-∞1x<br />5.limx->∞x3+4x+1x2+x-1<br />