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North CarolinaMaths

Functions and Exponential Models

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

What is the average rate of change of a function over an interval, and how do you compute it?

Calculate and interpret the average rate of change of a function over an interval from a graph or table (NC.M1.F-IF.6).
An NC Math 1 EOC answer on average rate of change (NC.M1.F-IF.6): the slope-of-the-secant formula, computing it from a table or graph, units in context, and why linear functions have a constant rate.
10 min answer →

How do linear, quadratic, and exponential functions differ, and why does exponential growth eventually win?

Compare linear, quadratic, and exponential functions across representations and observe that exponential growth eventually exceeds the others (NC.M1.F-LE.3, F-IF.9).
An NC Math 1 EOC answer on comparing function families (NC.M1.F-LE.3, F-IF.9): distinguishing linear, quadratic, and exponential by their patterns of change, comparing across tables and graphs, and why exponential growth eventually dominates.
11 min answer →

How do exponential functions model growth and decay, and how do you read their parameters?

Construct and interpret exponential functions for growth and decay, and interpret their parameters in context (NC.M1.F-LE.1, F-LE.2, F-LE.5).
An NC Math 1 EOC answer on exponential functions (NC.M1.F-LE.1, F-LE.2, F-LE.5): the form a times b to the x, growth versus decay, building from two points, and interpreting the initial value and growth factor.
11 min answer →

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

Define a function, use function notation to evaluate, and relate domain and range to a graph and context (NC.M1.F-IF.1, F-IF.2, F-IF.5).
An NC Math 1 EOC answer on functions (NC.M1.F-IF.1, F-IF.2, F-IF.5): the definition of a function, the vertical line test, evaluating with function notation, and reading domain and range from graphs and contexts.
11 min answer →

How do you read the key features of a graph and interpret them in context?

Interpret key features of graphs and tables (intercepts, increasing/decreasing, maxima/minima, end behavior) for linear, quadratic, and exponential functions (NC.M1.F-IF.4).
An NC Math 1 EOC answer on interpreting key features (NC.M1.F-IF.4): intercepts, intervals of increase and decrease, maximum and minimum, and end behavior, read from graphs and tables for linear, quadratic, and exponential functions.
11 min answer →

How do you write arithmetic and geometric sequences recursively and explicitly?

Recognize sequences as functions and write arithmetic and geometric sequences both recursively and explicitly (NC.M1.F-IF.3, F-BF.2).
An NC Math 1 EOC answer on sequences (NC.M1.F-IF.3, F-BF.2): the common difference and common ratio, explicit and recursive rules, sequences as functions on the integers, and finding a term.
11 min answer →

How do you solve a quadratic equation, and how do you choose a method?

Solve quadratic equations by inspection, square roots, factoring, and the quadratic formula, writing exact solutions (NC.M1.A-REI.4a).
An NC Math 1 EOC answer on solving quadratic equations (NC.M1.A-REI.4a): the zero-product property after factoring, taking square roots, the quadratic formula, and choosing the most efficient method.
11 min answer →