Types of functions. Let   n   be an integer, and let   a, a0, a1, ..., an, b, m   be real numbers.

A linear function is of the form   1.Insert here bxa   (a   is the fixed exponent or power)

A polynomial function is of the form   2.Insert here a function that can be constructed from polynomials using algebraic operations ( + ,   -,   ⋅,   ⁄,   xa) repeatedly.

A power function is of the form   3.Insert here p(x)⁄q(x), where   p   and   q   are polynomials

A root function is of the form   4.Insert here mx + b   (m   is the slope,   b   is the   y-intercept)

A rational function is of the form   5.Insert here sinx,   cosx,   tanx,   cscx,   secx,   cotx  

An algebraic function is   6.Insert here x1⁄n = n√(x)  

A basic trigonometric function is one of   7.Insert here anxn + an-1xn-1 + ⋅⋅⋅ + a2x2 + a1x + a0  

An exponential function is of the form   8.Insert here logax, where   a > 0   is the fixed base

A logarithmic function is of the form   9.Insert here ax, where   a > 0   (can you see why the base   a   should be positive?)

 

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Brief Instructions for solving this Text Puzzle: The puzzle pieces above have been shuffled, and your task is to move them around so that they end up in the correct position. Click a puzzle piece to select it, then click another puzzle piece to move (or swap) the selected piece to that particular position. When you think you are done, click on the Check button.

Text Puzzles by Peter Jipsen Chapman University