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Linear and Exponential Functions

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What is an arithmetic sequence, how do you write its explicit and recursive rules, and how is it a kind of linear function?

Construct and interpret arithmetic sequences with explicit and recursive rules, and connect them to linear functions whose domain is the integers (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on arithmetic sequences: the common difference, the explicit rule, the recursive rule, finding a specified term, and seeing an arithmetic sequence as a linear function defined on the integers.
9 min answer →

How do you tell a linear situation from an exponential one, and why does exponential growth eventually overtake linear growth?

Distinguish linear from exponential functions using constant difference versus constant ratio, and recognize that a quantity growing by equal factors over equal intervals is exponential (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on comparing linear and exponential models, using constant difference versus constant ratio in a table to classify a function, matching a context to the right model, and explaining why exponential growth eventually exceeds linear growth.
9 min answer →

What is an exponential function, how do growth and decay models work, and how do you read the initial value and the growth or decay rate?

Construct and interpret exponential functions, including growth and decay models, and identify the initial value and the growth or decay factor from an equation or context (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on exponential functions and growth and decay models, reading the initial value and base, converting a percent rate into a growth factor 1 plus r or a decay factor 1 minus r, and interpreting and evaluating exponential models.
11 min answer →

What makes a relation a function, how do you read and use function notation, and how do you find domain and range?

Determine whether a relation is a function, use function notation to evaluate and interpret functions, and identify domain and range from graphs and tables (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on the concept of a function, the vertical line test, evaluating and interpreting function notation, and reading domain and range from graphs, tables, and real contexts.
9 min answer →

What is a geometric sequence, how do you write its explicit and recursive rules, and how is it a kind of exponential function?

Construct and interpret geometric sequences with explicit and recursive rules, and connect them to exponential functions whose domain is the integers (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on geometric sequences: the common ratio, the explicit rule with a first term times the ratio to the n minus 1, the recursive rule, and seeing a geometric sequence as an exponential function on the integers.
9 min answer →

What makes a function linear, and how do you find and interpret the rate of change from a graph, a table, or a context?

Identify linear functions by their constant rate of change, compute average rate of change from tables and graphs, and interpret slope and intercept in context (A.FGR, Functional and Graphical Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on linear functions and rate of change: recognizing a constant rate of change as the signature of a linear function, computing rate of change from tables and graphs, and interpreting slope and intercept in real contexts.
9 min answer →