Functions

Understand that a function is a rule that assigns to each input exactly one output. • Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output. • Recognize functions given a table of values or a set of ordered pairs.

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

Identify linear functions from tables, equations, and graphs.

Analyze functions that model linear relationships. • Understand that a linear relationship can be generalized by 𝑦 = 𝑚𝑥 + 𝑏. • Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (𝑥, 𝑦) values or a graph. • Construct a graph of a linear relationship given an equation in slope-intercept form. • Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and 𝑦- intercept of its graph or a table of values.

Qualitatively analyze the functional relationship between two quantities. • Analyze a graph determining where the function is increasing or decreasing; linear or nonlinear. • Sketch a graph that exhibits the qualitative features of a real-world function.