Challenging Questions

Mathematics – Compulsory Part

Learning Unit: Exponential and logarithmic functions

Question M0-03-08

1. Sketch the graph of \( f(x) = \log_2x \) for \( x \in [0.125, 8] \). Label the points where \( x = 0.125, 0.5, 1, 2, 4, 8 \).
2. The function \( g(x) \) is obtained by reflecting \( f(x) \) over the \( y \)-axis and shifting it 2 units up. Write the equation of \( g(x) \).
3. Sketch the graph of \( g(x) \) on the same axes as \( f(x) \). Label the transformed points corresponding to \( x = 0.125, 0.5, 1, 2, 4, 8 \).
4. Solve the equation \( g(x) = 3 \) algebraically and verify your solution using the graph.

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