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- Understand the concept of a function and use function notation.
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# Understand the concept of a function and use function notation.

## Finer grained standards that are part of this one

understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).

use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.

recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.