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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 301 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
Tangent duration 9 minutes 54 seconds Tangent Tangent	Tangent Understanding the tangent function slope circles concepts in physics period cosine functions measure fourier analysis midline angle graph web colors cosine elementary algebra forward theta circle pi analytic geometry function asymptote notice greater vertical algebra differential topology optical spectrum increases tangent effects horizontal segment educational psychology shift equation traditional elementary geometry amplitude linear algebra elementary mathematics backward trigonometry sine unit thing times units From Carolyn James 334 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
4.3 Exponental Graphs duration 8 minutes 12 seconds 4.3 Exponental Graphs 4.3 Exponental Graphs	4.3 Exponental Graphs Exploring graphs of exponential functions growth estimate closer graph negative y-intercept approach function asymptote notice infinity notation increases effects rabbit horizontal bigger population increasing faster exponential equation limit exponentially positive approaching rabbits decay input values times factor output functions power metapopulations approaches From Carolyn James 293 plays 0
2.4 Transformations duration 10 minutes 43 seconds 2.4 Transformations 2.4 Transformations	2.4 Transformations Transformations of graphs of functions, including horizontal shifts, vertical shifts and reflections. operations constant height horizontal graph negative central nervous system units suppose transformation function direction parabola shifting effects input summarize subtract shift average months values positive coordinate output inside involves axis outputs shifts inputs baby unit point transformations column change vertex From Carolyn James 220 plays 0