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Drop That Bubble!!! Guess the missing then drop that bubble! © 2006 Doug Clarke Commutative Property Which Property? 3a+4=4+3a movement Associative Property Which Property? (2a+5)+3=2a+(5+3) ( ) changed Additive Identity Which Property? 10x+0 = 10x Multiplicative Identity Which Property? (20X)1 = 20x Additive Inverse -50a+50a = 0 Which Property? Multiplicative Inverse (1/5) (5) = 1 Which Property? Reflexive Property Which Property? 3x+2 = 3x+2 Symmetric Property Which Property? If 5+5=10, then 10 = 5+5 (If, then)(2 =) Distributive Property Which Property? 5 (a+4) = 5a +20 Transitive Property Which Property? If 4 = 2a and 2a = 5p, then 4=5p (If, then 3 =) Linear Function Type of Function? Equation has no exponents or symbols. Y= 3x +5 Substitution Property Which Property? If (5 + x) = Z and x = 2 then (5+2) =z Commutative Property Of Multiplication Which Property? (3+2x)5=5(3+2x) Multiplication Property Of Equality Which Property? If (x + 6) = 2 then 3(x+6) = 3(2) Quadratic Parabola Function? The equation has an exponent of 2. Y = 3x^2 - 6 Absolute Value Function? The equation has bars. Y = / 2x + 3/ Cubic Function Function? 3 Directions. Y = x^3+2 Exponential Function Function? The equation has an exponent that is a letter. (Hockey stick) Y = 3^x Roots, Zeros, Solutions X-intercepts All where the graph intersects the x-axis (4 answers) Factors Roots, x-intercepts, zeros, & solutions are Opposites of ___________. Write the equation for: If y varies Directly as x. Y= kx Write the equation for: If y varies As as y. Y = k/x Write the equation for: If y varies directly As x and inversely as z. Y= kx/z Formula for joint variation y/xy Has a pattern of addition: Arithmetic Series and Sequence Proportion for Direct Variation 1st x / 2nd x = 1st y/2nd y Has a pattern of multiplication: Geometric Series and Sequence Solutions for one graph are where? Where the graph touches the x axis. Where they touch each other Solutions for more than one graph are Where? Stat Edit Y= Plot 1 Zoom 9 Stat Calc What are the steps for finding the Line or curve of Best Fit? 100% Area under the curve is what %? 68% Within 1 standard deviation is what %? 95% Within 2 standard deviations is what %? 99.7% Within 3 standard deviations is What %? (lower, upper,mean,s.d.) To calculate % in an interval With normalcdf: Mean is 0 S.D is 1 When calculating a probability with A z-score the mean is ____and the Standard deviation is ____ Permutation Order matters (Math PRB #2) Combination Order does not matter (PRB #3) GCF When factoring Polynomials, look For the ____ 1st. (5x+2)(5x-2) Factor: 25x^2 - 4 (3y-1) (9y^2+3y+1) Factor: 27y^3-1 (5x+4) (25x^2-20x+16) Factor: 125x^3+64 Factor: 49x^2-25 (7x+5)(7x-5) Imaginary Numbers are also … Complex numbers < or > have ___ circles. Open When do graphs Have closed Circles? Equal signs = Solve by Factoring: X^2-2x-15=0 X=5 X=-3 Solve using the Quadratic Formula: 2x^2+4x-3=0 (-2+ or- square Root of 10)/2 3x^2-7x=-10 Has how many And what type of solutions? 2 imaginary or 2 complex Describe f(x)= x^2 could be Transformed to F(x) =-2x^2. Reflection across The x axis with A vertical Stretch of 2 Graph X^2-4x-5 Describe the Domain,range, Zeros, y-int. End Behavior. Domain: all real’s Range: y or = -9 Zero’s: -1 and 5 Y-int : (0,-5) E.B. As x app. Pos. inf. Y app Pos. inf. As x app Neg. if. Y app Pos. inf. The vertex Represents what Two letters? (h,k) If f(x)=3^x-3. Determine the Horizontal Asymptote, Domain, and Range. H.A: y=-3 Domain: All reals Range: y>-3 Ratio (r) = (Term)/(previous Term) To find inverse Given an Equation: 1) Interchange X and y 2) Solve for y If f(x)=1/(x+2) Describe the Domain, Range, & Asymptotes Domain: All Real Numbers except -2; Range: All Real Numbers Except 0; Asymptote: X=-2 Y=0