Home >> Science & Nature >> Science

How to Graph Translated Logs

A function is like a mathematical machine that takes an input and performs an action to create an output. There are many different types of functions, including trigonometric, logarithmic and exponential functions. A logarithmic function is the inverse function of an exponential, and it is used throughout science and engineering. The graph of Log(x) starts with a steep slope, but the slope decreases with increasing x. Any arbitrary function can have its graph translated using a simple rule.

Things You'll Need

Graph paper

Instructions

- 1
  Decide on the translation that needs to be performed for Log(x). Any arbitrary function f(x) can be translated to the right by "a" and up by "b" with the following transformation: y = f(x - a) + b. For the case of Log(x), this means that the translation would be y = Log(x - a) + b. If a = 3 and b = 2, then the graph will be transformed to the right by 3 and up by 2.
- 2
  Draw a table of the translated Log(x) values. Following the example:
  
  x = 5, Log(5 - 3) + 2 = 2.3
  
  x = 10, Log(10 - 3) + 2 = 2.85
  
  x = 15, Log(15 - 3) + 2 = 3.08
- 3
  Draw the graph axes on the graph paper. Label the x-axis "x" and the y-axis "Log(x - 3) + 2". Find the x and y values for the first point. Place a cross in this position. Plot the rest of the table. Using a ruler, draw a line between adjacent points. The graph should be translated to the right by 3 and up by 2.

Science