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11.1 Power Functions duration 8 minutes 56 seconds 11.1 Power Functions 11.1 Power Functions	11.1 Power Functions circles square constant power function rewrite flatter coefficient one-third binary operations elementary special functions examples geometric shapes proportional one-half inverse power types of functions squiggle three-halves negative mathematical notation pi analytic geometry function asymptote parabola algebra denominator polynomials increases effects multiplication bigger exponent times elementary geometry length values arithmetic positive exponentials conic sections functions cubed powers root x. run thing exponents halves p. notice n. From Carolyn James 296 plays 0
11.2 Polynomials duration 9 minutes 53 seconds 11.2 Polynomials 11.2 Polynomials	11.2 Polynomials function constant direction middle examine polynomial degree types of functions generic squiggle question negative vocabulary limit approach coefficient notice infinity power algebra outputs mathematical objects polynomials effects set theory leading quintic points values behavior positive term functions squiggles end 3x 2x run From Carolyn James 238 plays 0
Key Features of Rational Functions duration 13 minutes 7 seconds Key Features of Rational Functions Key Features of Rational Functions	Key Features of Rational Functions function horizontal ratio graph zeros rational y-intercept analytic geometry coefficient asymptote notice infinity vertical denominator polynomials long-term x-intercept summarize equation numerator equal behavior leading coordinate output piece effects hole thing functions asymptotes form coefficients degree minus power fourths From Carolyn James 300 plays 0
Rational Functions duration 11 minutes 16 seconds Rational Functions Rational Functions	Rational Functions coefficient real analysis elementary special functions numbers polynomial long-run types of functions leading divided negative elementary algebra rational microeconomics limit approach arithmetic function asymptote notice million infinity algebra denominator mathematical objects polynomials functions and mappings rational functions analytic functions effects horizontal bigger average numerator costs values analytic geometry behavior positive exponentials output elementary mathematics expression term asymptotes run cost functions 3x ratio drug grams graph outputs From Carolyn James 361 plays 0
11.3 Short Run Polynomials duration 13 minutes 8 seconds 11.3 Short Run Polynomials 11.3 Short Run Polynomials	11.3 Short Run Polynomials function multiplying point color one-third bounce short-run zero examples polynomial touches graph negative zeros factor coefficient notice linear degree effects squared- equation variations place behavior squiggle expression straight times root factors x. places cubed points roots From Carolyn James 193 plays 0
7.5 Sinusoidal Functions duration 11 minutes 31 seconds 7.5 Sinusoidal Functions 7.5 Sinusoidal Functions	7.5 Sinusoidal Functions Exploring transformations of sine and cosine functions coefficient concepts in physics period algebraically elementary special functions cos(bt) subtracting one-half transformations graph divided negative written cosine units formula audio engineering function notice complete algebra intercept shifting effects horizontal sound entire parentheses shift maximum trigonometry sinusoidal pi sine functions form place times fact sides b. half graphs From Carolyn James 280 plays 0
3.3 The Number e duration 9 minutes 58 seconds 3.3 The Number e 3.3 The Number e	3.3 The Number e Understanding the number e and its role in exponential functions sorting algorithms represent numerical analysis concepts in physics number approximation growth bacteria exponent function increase elementary algebra factor formula arithmetic coefficient triples algebra continuous purposes exponentials effects situation equations analytic geometry exponential double bottom equation equal times principle demography standard unix programs output model property equation rate base hours functions size power values sample notice past slope numbers From Carolyn James 330 plays 0
Part 1 Review: Solving Equations duration 12 minutes 12 seconds Part 1 Review: Solving Equations Part 1 Review: Solving Equations	Part 1 Review: Solving Equations Review of solving equations. square squared binary operations solution elementary special functions solutions distributive operation subtracting positive isolate quadratic elementary algebra fraction mathematical notation formula arithmetic difficult coefficient algebra factor mathematical objects polynomials simplify effects equations sides left-hand chemical processes squared- equation equal times right-hand solve elementary mathematics property expression root side capital 2x values minus hand r. x. 4ac front From Carolyn James 458 plays 0
Part 2 Review: Multiplying and Factoring… duration 10 minutes 13 seconds Part 2 Review: Multiplying and Factoring… Part 2 Review: Multiplying and Factoring Polynomials	Part 2 Review: Multiplying and Factoring Polynomials Multiplying and Factoring Polynomials mathematical multiplying rewrite process notice polynomial terms abstract algebra positive squared negative factoring combine mathematical notation elementary algebra arithmetic coefficient multiplied product multiple algebra factor polynomials effects multiplication squared- factorization times common definitions elementary mathematics property expression term cubed 3x minus 3a copies factors word numbers t. copy From Carolyn James 352 plays 0