Develop a t-chart if you want to fill in any other values. The number we multiply is called the base, so we can say: the logarithm of 8 with base 2 is 3 or log base 2 of 8 is 3 or the base-2 log of 8 is 3. Plot a vertical dashed line at x = 4, plot your intercepts and sketch the graph, understanding that the value of the function falls from left to right. To figure this out, it's helpful to rearrange the equation in a different form. The -2 at the end of the log means the graph is shifted 2 down. The x-intercept is the value of x when y = 0. The 2 in front means that the log means that the logs y value is multiplied by 2. Therefore, we should understand that the function decreases from the left, and falls asymptotically at x = 4. As an example, lets take f (x) log2 (3 (x2 - 9)) + 9. Since the asmptote is vertical, you only need to look at the horizontal transformations to determine its location. We can also understand that the behavior of the function is opposite of its parent function, log(x), since we effectively have log(-x). So, to find the vertical asymptote, we must look for the point at which the part inside the logarithm (its argument) would be 0. However, to simply sketch the graph, we need some intercepts and an understanding of the graph's behavior via asymptotes.įirstly, we should understand the function is asymptotic at x = 4, since the log(0) = inf. The graph of the logarithm base 2 crosses the x -axis at x 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log2(8) 3 and 23 8. You can certainly create a t-chart and evaluate the function for various x-values.
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