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Pre Calc 111 Review Sheet

# Pre Calc 111 Review Sheet - Pre Calc 111 Review Sheet...

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Pre Calc 111 Review Sheet Intervals Notation Set description (a,b) {x| a<x<b} [a,b] {x| a<=x<=b} [a,b) {x| a<=x<b} (a,b] {x| a<x<=b} (a,∞) {x| a<x} [a,∞) {x| a<=x} (-∞,b) {x| x<b} (-∞,b] {x| x<=b} (-∞,∞) All Real Numbers Laws of Exponents (A/b) -n = (b/a) n Properties of n th roots Definition of Rational Exponents A m/n = ( n √a) m Special Product Formulas 1. (A+B)(A-B) = A 2 -B 2 2. (A+B) 2 = A 2 +2AB+B 2 3. (A-B) 2 = A 2 -2AB+B 2 4. (A+B) 3 = A 3 +3A 2 B+3AB 2 +B 3 5. (A-B) 3 = A 3 -3A 2 B+3AB 2 -B 3 Special Factoring Formulas 1. (a + b)(a - b) = a 2 – b 2 where a, b >= 0 if n is even where a >= 0 and b > 0 if n is even (b not zero if n odd) if n is even if n is odd

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2. a 2 +2ab+b 2 = (a + b) 2 3. a 2 -2ab+b 2 = (a - b) 2 4. A 3 + B 3 = a 2 +2ab+b 2 (a + b) 2 5. A 3 + B 3 = a 2 -2ab+b 2 (a + b) 2 Linear Equation – ax + b = 0 Quadratic Equation – ax 2 + bx + c = 0 Completing the square Quadratic formula - Distance formula – Midpoint formula – Equation of a circle - (x - h) 2 + (y - k) 2 = r 2 If the center of the circle is at (0,0) then the equation is x 2 + y 2 = r 2 Slope of a line - m = (y 2 - y 1 ) / (x 2 - x 1 ) Point-slop form - y - y 1 = m(x - x 1 ) Equation of Horizontal and Vertical Lines: 1. an equation of a vertical line through (a,b) is x = a 2. an equation of a horizontal line through (a,b) is y = b
Parallel lines: two non-vertical lines are parallel if they have the same slope M 1 = d (B, C)/d (A, C) = d (E, F)/d (D, F) = M 2 Perpendicular lines: two lines with slopes m 1 and m 2 are perpendicular if m 1 m 2 = -1, their slopes are negative reciprocals: m 2 = - 1/m 1 Direct variation: y = kx (k cannot = 0) Inverse variation: y = k/x (k cannot = 0) Joint variation: z = kxy Graphs of functions: Domain: Range: Domain: Range: Domain: Range:

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Domain: Range: Average rate of change of f = Transformations of functions: 1. If the original (parent) function is y = f(x) , the reflection over the x-axis gives function h(x) , where h(x) = -f(x) .
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Pre Calc 111 Review Sheet - Pre Calc 111 Review Sheet...

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