AP® Precalculus: Logarithmic Functions — Drill 1

About This Drill

AP® Precalculus: Logarithmic Functions — Drill 1 is a Math practice drill covering logarithmic-functions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Build your understanding of logarithmic functions for the AP® Precalculus exam. These five questions cover domain and range, graph features including vertical asymptotes and intercepts, transformations of logarithmic functions, and the inverse relationship between exponential and logarithmic functions.

Questions in This Drill

1. What is the domain of the function \( f(x) = \log_3 (2x - 6) \)?
2. Which of the following correctly identifies a feature of the graph of \( f(x) = \log_2 (x + 4) \)?
3. The function g is defined by \( g(x) = -\log_5 (x - 2) + 1 \). Compared to the graph of \( f(x) = \log_5 x \), the graph of g is:
4. A population of bacteria is modeled by \( P(t) = 500 \cdot 2^t \), where t is time in hours. A researcher uses the inverse function to determine the time at which the population reaches a given size. Which of the following expresses t as a function of P?
5. Which of the following statements about the function \( f(x) = 2\log_{10}(x - 1) \) is correct?