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6. Exponential and Logarithmic Functions
Introduction to Logarithms
6. Exponential and Logarithmic Functions

Introduction to Logarithms: Videos & Practice Problems

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Problem 9Multiple Choice

For the given functions,
f(x) = log x
g(x) = - log(x - 1)
(i) Graph in the same cartesian plane
(ii) Identify all asymptotes
(iii) Identify Domain and Range


a) (i) Graph:Graph of f(x) and g(x) with asymptotes and points marked.
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x > 0; g(x): x > 0; Range f(x): all real values; g(x): all real values
b) (i) Graph:Graph of g(x) and f(x) with asymptotes and points marked.
(ii) Asymptotes f(x): x = 0, g(x): x = 0,
(iii) Domain f(x): x < 0; g(x): x < 0; Range f(x): f(x) > 0; g(x): g(x) > 0
c) (i) Graph:Graph of f(x) and g(x) with asymptotes and points marked.
(ii) Asymptotes f(x): x = 0, g(x): x = 1,
(iii) Domain f(x): x > 0; g(x): x > 1; Range f(x): all real values; g(x): all real values
d) (i) Graph:Graph of g(x) and f(x) with asymptotes and points marked.
(ii) Asymptotes f(x): x = 1, g(x): x = 0,
(iii) Domain f(x): x > 1; g(x): x > 0; Range f(x): all real values; g(x): all real values