Chapter 1 | Functions and Graphs
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CHAPTER 1 REVIEW
KEY TERMS
f ( x ) = ⎧ ⎩ ⎨ − x , x <0 x , x ≥0 a function involving any combination of only the basic operations of addition, subtraction,
absolute value function
algebraic function
base composite function cubic function multiplication, division, powers, and roots applied to an input variable x the number b in the exponential function f ( x ) = b x and the logarithmic function f ( x ) = log b x given two functions f and g , a new function, denoted g ∘ f , such that ⎛ ⎝ g ∘ f ⎞ ⎠ ( x ) = g ⎛ ⎝ f ( x ) ⎞ ⎠ a polynomial of degree 3; that is, a function of the form f ( x ) = ax 3 + bx 2 + cx + d , where a ≠0 a function decreasing on the interval I if, for all x 1 , x 2 ∈ I , f ( x 1 ) ≥ f ( x 2 ) if decreasing on the interval I
x 1 < x 2 for a polynomial function, the value of the largest exponent of any term the output variable for a function the set of inputs for a function a function is even if f (− x ) = f ( x ) for all x in the domain of f the value x in the expression b x a set of inputs, a set of outputs, and a rule for mapping each input to exactly one output the set of points ( x , y ) such that x is in the domain of f and y = f ( x )
degree dependent variable domain even function exponent function graph of a function horizontal line test
a function f is one-to-one if and only if every horizontal line intersects the graph of f , at most,
once
the functions denoted sinh, cosh, tanh, csch, sech, and coth, which involve certain
hyperbolic functions
combinations of e x and e − x
increasing on the interval I independent variable inverse function a function increasing on the interval I if for all x 1 , x 2 ∈ I , f ( x 1 ) ≤ f ( x 2 ) if x 1 < x 2 the input variable for a function for a function f , the inverse function f −1 satisfies f −1 ( y ) = x if f ( x ) = y the inverses of the hyperbolic functions where cosh and sech are restricted to the domain [0, ∞); each of these functions can be expressed in terms of a composition of the natural logarithm function and an algebraic function the inverses of the trigonometric functions are defined on restricted domains where they are one-to-one functions a function that can be written in the form f ( x ) = mx + b a function of the form f ( x ) = log b ( x ) for some base b >0, b ≠1 such that y = log b ( x ) if and only if b y = x A method of simulating real-life situations with mathematical equations the function f ( x ) = e x inverse hyperbolic functions inverse trigonometric functions linear function logarithmic function mathematical model natural exponential function
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