Final answer:
Poly's observation that exponential and logarithmic functions are opposites stems from the fact they are inverse of each other, with exponential functions represented by y = b^x and logarithmic functions by y = log_b(x). Exponential graphs grow rapidly while logarithmic graphs increase slowly. Log-log plots are used to linearize exponential relationships such as those found in the frequency and wavelength of electromagnetic radiation.
Step-by-step explanation:
When Poly suggests that the graphs of exponential and logarithmic functions are complete opposites, she is recognizing that they are inverse functions of each other. Exponential functions are characterized by a constant ratio of change and have equations of the form y = b^x, where b is the base. These functions grow rapidly and their graphs exhibit a characteristic 'J-shaped' curve. On the other hand, logarithmic functions, which have the form y = log_b(x), increase slowly and their graphs are shaped like a backwards 'J'. The relationship between exponential and logarithmic functions is further illustrated by the fact that logarithms are used to 'undo' the effect of exponentiation — for example, if y = b^x, then log_b(y) = x. This inverse relationship is evident when reflecting the graph of an exponential function over the line y = x, which would produce the graph of its corresponding logarithmic function.
When dealing with the log-log plot, both axes are scaled logarithmically, which is useful for representing relationships that are exponential in nature. This type of plot is frequently used to depict phenomena such as the wavelength and frequency relationship of electromagnetic radiation, where both quantities span several orders of magnitude. A log-log plot can linearize the curve of an exponential relationship, thereby simplifying the interpretation and comparison of data.