Investigation Three: More Nonlinear Models

Enter a set of data points, then derive a function to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Graphs, Modeling, Statistics, Trigonometry

Related Topics: algebra, cartesian coordinate, coordinate, coordinate plane, coordinate system, cosecant, cosine, cotangent, curve fitting, data plot, deviations, exponential, exponents, function properties, functions, graph, grouping, integers, intervals, inverse, linear equations, linear functions, logarithm, multiplication, parabola, polynomial, positive part of the operand, pre-calculus, range, secant, sine, slope, tangent, trigonometry

A more advanced version of Slope Slider, this activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Graphs, Trigonometry

Related Topics: algebra, bell curve, calculus, cartesian coordinate, coordinate plane, coordinate system, cosine, decimals, exponential, flyer, function properties, functions, graph, intervals, inverse, linear equations, linear functions, lines, logarithm, parabola, polynomial, pre-calculus, range, sine, slope, tangent, translation, trigonometry

Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs. Function Machine is one of the Interactivate assessment explorers.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Discrete

Related Topics: addition, algebra, arithmetic, assessment, function machine, functions, input, integers, linear equations, multiplication, output, subtraction

Students can create graphs of functions entered as algebraic expressions -- similar to a graphing calculator.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Graphs, Trigonometry

Related Topics: algebra, calculus, cartesian coordinate, coordinate plane, cosecant, cosine, cotangent, functions, graph, inverse, linear equations, linear functions, logarithm, parabola, polynomial, positive part of the operand, pre-calculus, range, secant, sine, slope, tangent, trigonometry

Create graphs of functions and sets of ordered pairs on the same coordinate plane. This is like a graphing calculator with advanced viewing options.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Graphs, Statistics, Trigonometry

Related Topics: algebra, calculus, cartesian coordinate, coordinate, coordinate plane, coordinate system, cosecant, cosine, cotangent, curve fitting, data plot, exponential, exponents, function properties, functions, graph, graph theory, intervals, linear equations, linear functions, logarithm, parabola, polynomial, positive part of the operand, pre-calculus, range, secant, sine, slope, tangent, trigonometry

Plot ordered pairs on the graph, and they will be connected in the order that they are input. This enables you to decide how the pairs should be connected, rather than having the computer connect them from left to right.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Geometry, Graphs, Statistics

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, data plot, graph, lines, vertical line test

Plot a bivariate data set, determine the line of best fit for their data, and then check the accuracy of your line of best fit.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Graphs, Statistics

Related Topics: calculus, cartesian coordinate, coordinate plane, correlation, curve fitting, data plot, deviations, residual, statistics

Plot ordered pairs of numbers, either as a scatter plot or with the dots connected. Points are connected from right to left, rather than being connected in the order they are entered.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Geometry, Graphs, Statistics

Related Topics: cartesian coordinate, coordinate plane, coordinate system, data plot, decimals, graph

Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Geometry, Graphs, Number and Operations

Related Topics: complex number, coordinate plane, coordinate system, exponents, fractals, functions, graph, infinity, iteration, julia set, mandelbrot set, recursion, recursive functions, sets