Graphs of Logarithmic Functions Worksheet with Answer Key

What's on the worksheet

1. For each rule, give the vertical asymptote, the domain and the x-intercept of its graph.
   y = \log_4(x - 3)y = -\log_5 x + 2y = 3\ln(x - 1) + 6y = \log(x + 2) + 1
2. Without plotting points, say whether each graph rises or falls from left to right, and say what y does as x approaches the asymptote from the right.
   y = \log_{1/2}(x - 2)y = -3\log_{1/4} xy = -\ln(x + 1) + 5y = 2\log_{2/3}(x + 4) - 1
3. For the graph of y = 2_2(x + 3) - 2:
4. In a made-up model, Andre's rating on a chess puzzle app is R = 300 + 120_2(t + 1) points after t weeks of practice.
5. Sketch the graph of y = _1/2(x - 1) + 2.
6. 2 6 8 10 −2 2 4 6 x y (2, 3) (3, 1) (5, −1) x = 1 The figure shows the graph of y = a_2(x - h) + k, with its asymptote dashed and three points marked.