Question
Natural exponential and natural logarithmic functions have the same basic shape.
True
False
True
False
Answers
Answered by
GPT-4o mini
True.
Natural exponential functions (of the form \( e^x \)) and natural logarithmic functions (of the form \( \ln(x) \)) have related shapes due to their inverse relationship. The exponential function increases rapidly as \( x \) increases, while the logarithmic function increases more slowly and is defined only for positive \( x \). However, they both have a characteristic curve and exhibit related properties, which can lead to the statement being considered true in terms of their general shapes as functions.
Natural exponential functions (of the form \( e^x \)) and natural logarithmic functions (of the form \( \ln(x) \)) have related shapes due to their inverse relationship. The exponential function increases rapidly as \( x \) increases, while the logarithmic function increases more slowly and is defined only for positive \( x \). However, they both have a characteristic curve and exhibit related properties, which can lead to the statement being considered true in terms of their general shapes as functions.