This study guide covers topics in precalculus including: 1) Examples of natural numbers, integers, rational numbers, and real numbers. 2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x). 3) Finding inverses of functions and verifying inverses by composition. 4) Operations on complex numbers including plotting, finding modulus, distance, midpoint, addition, subtraction, multiplication, and division. 5) Graphing functions, classifying function types, and stating domains and ranges. 6) Finding limits of functions as x approaches values.

1. Precalculus<br />Exam 1 Study Guide<br />Be able to provide two examples for each of the following:<br />Natural numbers

2. Integers

3. Rational numbers

4. Real numbers

5. Pure imaginary numbers

6. Complex numbersComposition 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 />