Chapter Outline
In Unit 6, “Graphs, Tables, and Patterns in Functions,” we explore how to interpret and analyze data through various mathematical frameworks. This unit guides you through the process of using graphs to understand the key aspects of a function, with special emphasis on employing interval notation. It also covers how to make predictions about a function’s behavior by examining tables of values. Additionally, you will learn to recognize and describe patterns in numerical sequences, determining whether they are arithmetic or geometric, and develop skills in writing and using recursive rules for sequences.
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6.1
Analyzing Graphs
Learning Objectives
By the end of this section, you will be able to:
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analyze graphs of functions to determine where the function is positive, negative, or zero and identify intervals of increase or decrease.
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determine local maximum and minimum values of a function from its graph.
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use a graph to find and interpret the function’s input and output values and understand its behavior as inputs increase or decrease.
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apply graph analysis to real-world problems, determining appropriate domains and analyzing end behavior and intercepts within specific contexts.
6.2
Analyzing Tables
Learning Objectives
By the end of this section, you will be able to:
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determine the behavior of a function from a table, identifying intervals where the function is increasing, decreasing, positive, or negative.
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analyze tables to find x-intercepts, y-intercepts, and local maximum and minimum values.
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use tables to predict potential turning points and end behavior of a function.
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apply my understanding of table analysis to investigate real-world problems, interpreting functional relationships and their graphical representations.