Mathematical Methods · Unit 2 · Logarithms and logarithmic functions · Logarithmic functions
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Consider the function $f(x) = 2 + \log_{3}(x - 1)$ for $x > 1$. (a) State the equation of the vertical asymptote. (1 mark) (b) Find the $x$-intercept of the graph, giving your answer in exact form. (1 mark) (c) Determine the coordinates of the point where the graph passes through $x = 4$. (1 mark)
Consider the function \( f(x) = 2\log_e(x - 3) + 1 \) defined on its maximal domain. (a) State the domain and range of \( f \). (1 mark) (b) Determine the coordinates of the \( x \)-intercept and \( y \)-intercept of \( f \), if they exist. Express answers in exact form. (2 marks) (c) State the equation of the vertical asymptote of \( f \) and explain the mathematical reasoning that determines its position. (1 mark)
The graph of $y = \log_3(x - 2) + 1$ is obtained by applying transformations to the parent function $y = \log_3(x)$. Which of the following correctly describes the graph of the transformed function?