The basic graph of is subjected to the three separate transformations described below.
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The basic graph of y=log3x is subjected to the three separate transformations described below.
(a) Replace x by x−4. Explain the effect of this change on the position of the graph, write the new equation, and give the new coordinates of the point that was originally (1,0) as well as the new equation of the asymptote.
(b) Starting again with y=log3x, multiply the whole expression by −1. Describe the resulting reflection and give the equation of the transformed curve. Comment on its domain and range.
(c) Starting again with y=log3x, add 2 to obtain y=log3x+2. Explain the vertical shift produced, giving the new coordinates of the key point and the new range.
(d) Summarise, in about four sentences, how horizontal shifts, vertical shifts, and reflections about the coordinate axes affect any logarithmic curve of the form y=logax.