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Lesson 4

1. Lesson 4

1.6. Explore 2

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

In Try This 2 you may have found that the parameters a, b, h, and k change the graph of a logarithmic function in the form in the following ways.

 

Parameter

Transformation

Example
a
  • There is a vertical stretch by a factor of |a| about the x-axis.
  • When a < 0, there is a reflection in the x-axis.
 This is a graph of 3 logarithmic functions. The equations of the functions are y equals 3 times log base 10 of x, y equals log base 10 of x, and y equals negative 2 times the log base 10 of x.
b
  • There is a horizontal stretch by a factor of about the y-axis.
  • When b < 0, there is a reflection in the y-axis.
 This is a graph of 3 logarithmic functions. The equations of the functions are y equals log base 10 of negative 3 times x, y equals log base 10 of 4 times x, and y equals log base 10 of x.
h
  • There is a horizontal translation of h units left or right. The h-value affects the vertical asymptote.
 This is a graph of 3 logarithmic functions. The equations of the functions are y equals log base 10 of x plus 4, y equals log base 10 of x, and y equals log base 10 of x minus 3.
k
  • There is a vertical translation of k units up or down.
 This is a graph of 3 logarithmic functions. The equations of the functions are y equals log base 10 of x and then 4 is added, y equals log base 10 of x, and y equals log base 10 of x and then 3 is subtracted.

 

You may have also noticed in Try This 2 that the parameters h and b affect the domain:

  • The h-value translates the domain left or right.
  • If the b-value is negative, the graph is reflected in the y-axis, and so the domain is reflected.

The range is unchanged and is all real numbers.

You may find it helpful to look at Multiple Transformations from Try This 2 as you review this chart.