MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
An unknown logarithmic function has equation y=logax with a>1. The graph is known to pass through the point (4,2).
(i) Determine the value of the base a.
(ii) State whether the graph is concave up or concave down and whether it is increasing or decreasing on (0,∞).
(iii) Write the equation of the vertical asymptote and the coordinates of the x-intercept of the graph.
(iv) On ruled graph paper, draw a neat sketch of the graph showing the asymptote, the intercept, and the given point. (A qualitative sketch is sufficient; exact scale is not required.)