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alg 1 unit 2 resources
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Transcript
Unit 2: Linear & Exponential Functions
This unit broadens understanding of arithmetic and geometric sequences from the first unit to include linear and exponential functions with a continuous domain. It continues building fluency in writing explicit function rules for both linear and exponential functions. It analyzes the context to determine if the relationship being described is continuous or discrete, evoking discussions about the domain of a function and how it affects the graph and other representations of the function. First, it provides real-world scenarios and contexts that can be modeled more closely with either discrete or continuous mathematical models to support the conceptual development of each type of model and how it relates to domain, extends understanding about arithmetic and geometric sequences to support work with linear and exponential functions, making connections between discrete sequences and continuous functions, to see the need for distinguishing between different domains for functions, as well as for knowing which type of function will be the best model for the situation being considered. Second, it develops a connection between rational exponents and radicals. Instead of calculating the constant ratio between consecutive terms, it considers what occurs between two consecutive terms. For example, if the domain of the sequence is continuous, it makes sense to calculate the value of the function halfway between two consecutive terms or a third of the way. It uses understanding of rational exponents and roots to find equivalent forms of algebraic expressions. Lastly, it focuses on calling out characteristics of linear and exponential functions and their equations, like how to write equivalent equations for both linear and exponential relationships, and how to compare the growth rates of linear and exponential relationships. It also introduces the point-slope form of the equation of a line and comparing the use of different forms of linear equations for different purposes.