The semi-log graph paper shown below has a linear scale
along the horizontal axis and a logarithmic scale along the vertical axis; thus it is called a "semi-log" graph. The vertical scale on this piece of graph
paper has three “decades”. The values
start at 1 and increase until 10, then increase in multiples of 10 until 100. The set
beyond 102=100 increases by units of 100 until 1000, and so forth. You’ll notice that the lines are not linearly
spaced. Notice how the vertical axis is
labeled in the graph below.
In your previous graphing experience, graphs of data are
plotted on paper that has linear scales on both the horizontal and vertical
axes. However, this is a different kind
of scale that is very different. This exercise will help you to see some of the
reasons for this.
And now, your personal exploration to increase comprehension:
- Make a table of values for
the function F(x) = 2^x with values of x from x = 0 to x = 9. Plot the graph of this function on the semi-log graph
paper. Use caution when plotting
the F(x) =y values since the vertical scale is not linear. Draw a smooth curve through the points
and label the equation of the function on the graph. Do the same for G(x)=3x.
- Make a table of values for
the function f(x) = 2x with values of x from x = 0 to x = 9. Plot the graph
of this function on the semi-log graph paper. Again, use caution when plotting the f(x) = y values since the
vertical scale is not linear. Draw
a smooth curve through the points and label the equation of the function
on the graph. Do the same for g(x)=3x.
- Briefly describe the differences between the graphs on a semi-log paper and on the rectangular graph paper you’ve previously used. What are some reasons why you might want to graph data on semi-log paper? What are some advantages and disadvantages? How could a graph that has a logarithmic scale be misleading?
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