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Week 3 Power Functions Presentation

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Week 3 5.2 Power Functions A function with a single term that is the product of a real number (coefficient) and a variable raised to a fixed number f(x) = kxp K and p are real numbers and K is the coefficient f(x)=2x is not a power function because the power is not constant End Behavior of Power Functions As the power increases, the graph is flatter towards the origin (0,0) and becomes steeper (narrowing towards the y-axis) EVEN POWER: We refer to the behavior of a power by saying “x approaches infinity” (also written as x → ∞). We can say x is increasing without bound (without limitations, goes on forever). Looks like parabola ODD POWER: Graph goes up in one on the positive side of the y-axis and goes down on the negative side of the y-axis Polynomial Functions An equation is a polynomial function IF: - EXAMPLE 5 f(x) = 3 + 2x2 - 4x3 The exponent is a positive whole number Degree = 3 3 The exponent is not negative or a variable Leading Term = -4x Leading Coefficient = -4 such as x DEGREE: Highest power in function LEADING TERM: Term with highest power LEADING COEFFICIENT: coefficient of the leading term h(x) = 6p - p3 - 2 Degree = 3 Leading Term = -p3 Leading Coefficient = -1 Put the Example in General Form, Find Degrees, and End Behavior f(x) = -3x2 ( x - 1 ) ( x + 4 ) f(x) = -3x2 ( x2 + 4x - 1x - 4 ) f(x) = -3x2 ( x2 + 3x - 4) f(x) = -3x4 - 9x3 + 12x2 . General Form f(x) = -3x4 - 9x3 + 12x2 Leading Term = -3x4 so Degree is 4 Degree is Even (4) an ...
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