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Chapter 1 | Functions and Graphs
natural logarithm
number e the function ln x = log e x as m gets larger, the quantity (1+(1/ m ) m gets closer to some real number; we define that real number to be e ; the value of e is approximately 2.718282 a function is odd if f (− x ) =− f ( x ) for all x in the domain of f a function f is one-to-one if f ( x 1 ) ≠ f ( x 2 ) if x 1 ≠ x 2 a function is periodic if it has a repeating pattern as the values of x move from left to right a function that is defined differently on different parts of its domain equation of a linear function indicating its slope and a point on the graph of the function a function of the form f ( x ) = a n x n + a n −1 x n −1 +…+ a 1 x + a 0 a function of the form f ( x ) = x n for any positive integer n ≥1 a polynomial of degree 2; that is, a function of the form f ( x ) = ax 2 + bx + c where a ≠0 for a circular arc of length s on a circle of radius 1, the radian measure of the associated angle θ is s the set of outputs for a function a function of the form f ( x ) = p ( x )/ q ( x ), where p ( x ) and q ( x ) are polynomials a subset of the domain of a function f a function of the form f ( x ) = x 1/ n for any integer n ≥2 the change in y for each unit change in x equation of a linear function indicating its slope and y -intercept the graph of a function f is symmetric about the origin if (− x , − y ) is on the graph of f whenever ( x , y ) is on the graph the graph of a function f is symmetric about the y -axis if (− x , y ) is on the graph of f whenever ( x , y ) is on the graph a table containing a list of inputs and their corresponding outputs a function that cannot be expressed by a combination of basic arithmetic operations a shift, scaling, or reflection of a function functions of an angle defined as ratios of the lengths of the sides of a right triangle an equation involving trigonometric functions that is true for all angles θ for which the functions in the equation are defined given the graph of a function, every vertical line intersects the graph, at most, once when a real number x is a zero of a function f , f ( x ) =0 KEY EQUATIONS • Composition of two functions ⎛ ⎝ g ∘ f ⎞ ⎠ ( x ) = g ⎛ ⎝ f ( x ) odd function one-to-one function periodic function piecewise-defined function point-slope equation polynomial function power function quadratic function radians range rational function restricted domain root function slope slope-intercept form symmetry about the origin symmetry about the y -axis table of values transcendental function transformation of a function trigonometric functions trigonometric identity vertical line test zeros of a function
⎞ ⎠ • Absolute value function f ( x ) = ⎧ ⎩ ⎨ − x , x <0 x , x ≥0
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