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TennesseeMaths

Functions

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you calculate and interpret the average rate of change of a function over an interval?

Calculate and interpret the average rate of change of a function over a specified interval from a graph or table (TN A1.F.IF.C.6).
A TNReady Algebra I answer on average rate of change (TN A1.F.IF.C.6), the change-in-output over change-in-input formula, computing it from tables and graphs, and interpreting it as a slope.
9 min answer →

How do you compare linear, quadratic, and exponential functions across tables, graphs, and equations, and recognize which models a situation?

Compare properties of linear, quadratic, and exponential functions represented in different ways, and identify the family that models a situation (TN A1.F.IF.D.9, A1.F.LE.A.3).
A TNReady Algebra I answer on comparing function families (TN A1.F.IF.D.9, A1.F.LE.A.3), identifying linear, quadratic, and exponential behavior from tables and graphs, and comparing rates of growth.
10 min answer →

How do you model and graph exponential growth and decay, and how do you tell an exponential situation from a linear one?

Construct and graph exponential functions, distinguish exponential from linear growth, and interpret growth and decay models (TN A1.F.IF.D.7e, A1.F.LE.A.1, A1.F.LE.A.2).
A TNReady Algebra I answer on exponential functions (TN A1.F.IF.D.7e, A1.F.LE.A.1-2), the growth and decay models, the meaning of the base, graphing with the y-intercept and asymptote, and linear versus exponential.
11 min answer →

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

Understand that a function assigns each input exactly one output, use function notation to evaluate functions, and identify domain and range (TN A1.F.IF.A.1, A1.F.IF.A.2, A1.F.IF.C.5).
A TNReady Algebra I answer on the definition of a function (TN A1.F.IF.A.1-2), the vertical line test, evaluating with function notation, and identifying domain and range from graphs and tables.
10 min answer →

How do you read and interpret the key features of a function's graph, such as intercepts, intervals of increase or decrease, and maximums or minimums?

Interpret key features of graphs and tables (intercepts, intervals of increase and decrease, maxima and minima, end behavior) in terms of the quantities they model (TN A1.F.IF.C.4).
A TNReady Algebra I answer on interpreting key features (TN A1.F.IF.C.4), x- and y-intercepts, intervals of increase and decrease, maxima and minima, and end behavior, in the context of a model.
10 min answer →

How do you write arithmetic and geometric sequences explicitly and recursively, and how are they related to linear and exponential functions?

Write arithmetic and geometric sequences both recursively and explicitly, and recognize sequences as functions on the integers (TN A1.F.BF.A.2, A1.F.IF.B.3).
A TNReady Algebra I answer on arithmetic and geometric sequences (TN A1.F.BF.A.2, A1.F.IF.B.3), the explicit and recursive forms from the reference sheet, common difference versus common ratio, and the link to linear and exponential functions.
10 min answer →

How do you write the equation of a line from a slope and a point, two points, a graph, or a context?

Write linear functions and equations of lines using slope-intercept and point-slope form, from a graph, two points, or a real-world description (TN A1.F.LE.A.2, A1.A.CED.A.2).
A TNReady Algebra I answer on writing linear functions (TN A1.F.LE.A.2, A1.A.CED.A.2), the slope formula, slope-intercept and point-slope forms, and building a line from two points or a context.
11 min answer →