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Basic Functions

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Linear and Exponential Functions Power Functions Logarithmic Functions Trigonometric Functions

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A population of 200 worms increases at the rate of 5 worms per day. How many worms are there after a fifteen days? Linear Function

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Linear Functions Slope m=rise/run Slope m=rise/run Change on y when x increases by 1 Y intercept or value when x=0

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Exercise Find the equation of the line passing through the points (-2,1), (4,5) Point: Slope: Point-Slope form Slope-Y intercept form

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Exponential Growth A population of 200 worms increases at the rate of 5% per day. How many worms are there after fifteen days?

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Exponential Growth Population of Mexico City since 1980 (t=0) t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999 Is this a linear function?

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t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999

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Equation from Table t (years after 1980 0123 P(t) (in millions) 67.3870.918782172.762670574.6544999 Initial Population t=0 Grows at 2.6% per year (100%+2.6% next period) 1.026 = growth factor 1=1+0.026 Grows at 2.6% per year (100%+2.6% next period) 1.026 = growth factor 1=1+0.026 What is the doubling time?

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1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Common domain – Intercepts – Dominance What do you need to know about the basic functions?

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Power Functions

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Positive Even Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes

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Positive Odd Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Negative Even Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Negative Odd Powers 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Positive Even Roots 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Positive Odd Roots 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Exponential Growth 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Exponential Decay 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Natural Log Function 1.Shape 2.Domain 3.End behavior 4.Intercepts with coordinate axes 5.Compare them – Intercepts – Dominance

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Sine and Cosine

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COMPARING FUNCTIONS Consider the functions For which values in their common domain is Toward the end points of the common domain which of the two functions dominate?

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Common domain Graphical Solution Algebraic Solution number line

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Dominance Comparing functions toward the end points of their common domains their common domains

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