Module 6: Lesson 4

 

Self-Check 3

 

“Your Turn” from “Example 3” on page 388 of the textbook

 

Method 1: Compare with the Graph of y = log4 x.

 

The key point (4, 1) on the graph of y = log4 x has become the image point (4, −3) on the red graph. Thus, the red graph can be generated by vertically stretching the graph of y = log4 x about the x-axis by a factor of 3 and then by reflecting the graph about the y-axis. The red graph can be described by the equation y = −3log4 x.

 

Method 2: Use Points and Substitution

 

There is a vertical stretch about the x-axis and a reflection about the x-axis. This means that the equation of the red graph will be of the form y = −alog4  x. Substitute the coordinates of a point on the red graph, such as (4, −3), into the equation and solve for a.

 

 

This means that the a-value is 3 and that the red graph can be described by the equation y = −3log4 x.

 

Adapted from Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.

© 2012 Alberta Education