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FloridaMaths

Exponential and Nonlinear Functions

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you tell linear, quadratic, and exponential functions apart from a table, an equation, or a graph, and why does exponential growth eventually overtake the others?

Distinguish among linear, quadratic, and exponential functions using their rates of change from tables, equations, and graphs, and recognize that a quantity growing exponentially eventually exceeds one growing linearly or quadratically (MA.912.F.1.6, MA.912.AR.5.6).
A B.E.S.T. Algebra 1 EOC answer on distinguishing function families (MA.912.F.1), constant differences for linear, constant second differences for quadratic, constant ratios for exponential, and why exponential growth eventually dominates.
10 min answer →

How do you write and use exponential growth and decay models, and interpret the initial value and the growth or decay rate?

Write, evaluate, and interpret exponential functions that model growth and decay, identifying the initial value and the growth or decay factor and rate (MA.912.AR.5.4, MA.912.F.1.6).
A B.E.S.T. Algebra 1 EOC answer on exponential models (MA.912.AR.5), the growth and decay forms y = a(1 + r)^t and y = a(1 - r)^t, the initial value, the growth or decay factor, and interpreting in context.
11 min answer →

How do you graph an exponential function and identify its y-intercept, horizontal asymptote, domain, range, and growth or decay behavior?

Graph exponential functions and identify key features including the y-intercept, the horizontal asymptote, domain, range, and whether the function is increasing or decreasing (MA.912.F.1.3, MA.912.AR.5.6).
A B.E.S.T. Algebra 1 EOC answer on graphing exponentials (MA.912.F.1, AR.5), the y-intercept at the initial value, the horizontal asymptote at y = 0, the domain and range, and growth versus decay shape.
10 min answer →

How do you graph and read key features of square-root, cube-root, absolute-value, and piecewise functions?

Graph and interpret key features of square-root, cube-root, absolute-value, and piecewise-defined functions, including domain restrictions and points of interest (MA.912.F.1.1, MA.912.AR.4.3).
A B.E.S.T. Algebra 1 EOC answer on other nonlinear functions (MA.912.F.1), the shapes and domains of square-root, cube-root, absolute-value, and piecewise functions, and reading key features.
10 min answer →