ch.1 Linear Functions and Change

ch.1 Linear Functions and Change - Chapter 1 Linear...

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Chapter 1 Linear Functions and Change 1.1 Functions and function notation
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Key Points • The definition of a function • Numerical, graphical, symbolic, and verbal representaions • The vertical line test • Basic function concepts and language
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2 ( ) f x x = 2 ( ) f x x =
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Definition of a Function • A function is a rule that assigns to each input a unique output. The inputs and outputs are also called variables. • Each input yields one and only one output, but the same output can be associated with several inputs.
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Function Notation • Recognize and translate the verbal phrase “Q equals f of t”. Q is a function of t • In the function Q = f(t), identify the input and the output. • Q does not have to be related to t by a formula. The function may be given by a table, a graph, or a verbal description.
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How to Tell if a Graph Represents a Function: Vertical Line Test Vertical Line Test : If there is a vertical line which intersects a graph in more than one point, then the graph does not represent a function. Vertical Line Test : If there is a vertical line which intersects a graph in more than one point, then the graph does not represent a function. Functions Modeling Change: A Preparation for Calculus, 4th
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How to Tell if a Graph Represents a Function: Vertical Line Test Visualizing the Vertical Line Test Functions Modeling Change: A Preparation for Calculus, 4th No matter where we draw the vertical line, it will intersect the red graph at only one point, so the red graph represents a function. But the vertical line intersects the blue graph twice, so the blue graph does not represent a function. 4 2 2 4 x 4 2 2 4 y vertical line
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2, 6,10,14, 20, 26,36
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Chapter 1 Linear Functions and Change 1.2 Rate of Change
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Rate of Change The table below shows the populations (in thousands) of three towns as functions of the year. In each case the population is determined at the end of the year. Town 1980 1981 1982 1983 1984 1985 P 10 14 18 22 26 30 Q 10 17 23 27 29 30 S 10 12 15 19 24 30
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Rate of Change of a Function The average rate of change , or rate of change , of Q with respect to t over an interval is The average rate of change , or rate of change , of Q with respect to t over an interval is Functions Modeling Change: A Preparation for Calculus, 4th t Q t Q = = in Change in Change interval an over change of rate Average
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Graphs of Increasing and Decreasing Functions The graph of an increasing function rises when read from left to right. The graph of a decreasing function falls when read from left to right. Functions Modeling Change: A Preparation for Calculus, 4th 0 5 1 0 1 5 2 0 x 1 2 3 4 5 y Decreasing function Increasing function
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Rates of Change for Increasing and Decreasing Functions If Q = f ( t ), • If f is an increasing function, then the average rate of change of Q with respect to t is positive on every interval. • If
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This note was uploaded on 04/04/2012 for the course MATH 2412 taught by Professor Staff during the Spring '08 term at Austin CC.

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ch.1 Linear Functions and Change - Chapter 1 Linear...

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