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The first chapter is primarily a review of topics that youve seen in Pre-Calculus and other classes. If you are having trouble with any of these topics, ask RIGHT AWAY – these topics form the foundation of everything that we will do this year.

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Functions Def. A function is a relationship where no two points have the same x-coordinate. Each x-coordinate is associate with at most one y-coordinate The graph passes the vertical line test Domain all possible values of x where the function is defined. Range all possible values that the function attains

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Ex. Find the domain and range. a) b)

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If y is proportional to x, then y = kx. If y is inversely proportional to x, then

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Def. A piecewise function is a function whose equation depends of the value of x where it is being evaluated. Ex. Graph

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The absolute value function is an example of a piecewise function:

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Linear Functions Either form is fine, you dont need to simplify your equation.

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Ex. Find the equation of the line that contains (-2,1) and (2,3).

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Ex. Find the equations of the lines parallel to and perpendicular to y – 5x = 3 that contain the point (2,1).

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Exponential Functions P 0 = initial value a = base k = continuous growth rate r = annual growth rate Laws of Exponents can be found on H p. 21

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Ex. The population of Quahog is 10,000,000 and it has an annual growth rate of 2%. Find the doubling time.

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Ex. Assume that housing prices grow exponentially and that Mr. Burns mansion cost $50,000 in 1970 and $200,000 in 1990. If t is years since 1970, write an equation that represents the cost of the mansion as a function of t. How much would the house cost in 2012?

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