TY - JOUR

T1 - Secants, tangents, rotations, and reflections

AU - Maltenfort, Michael Brian

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Given the graph of a continuous function on an interval, if we know the slopes of all the secant lines, then we can determine which rotations and reflections of the graph are also graphs of functions and, for those that are, whether the new functions are one-to-one. Provided that the original function is differentiable on the interior of the interval, we can determine the slopes of all secant lines by calculating the range of the function's derivative, provided that we know any subintervals where the function is linear.

AB - Given the graph of a continuous function on an interval, if we know the slopes of all the secant lines, then we can determine which rotations and reflections of the graph are also graphs of functions and, for those that are, whether the new functions are one-to-one. Provided that the original function is differentiable on the interior of the interval, we can determine the slopes of all secant lines by calculating the range of the function's derivative, provided that we know any subintervals where the function is linear.

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U2 - 10.4169/college.math.j.46.1.24

DO - 10.4169/college.math.j.46.1.24

M3 - Article

AN - SCOPUS:84975867836

SN - 0746-8342

VL - 46

SP - 24

EP - 34

JO - College Mathematics Journal

JF - College Mathematics Journal

IS - 1

ER -