Lesson 4

Discover

 

Recall from Lesson 3 that y = log10x is equivalent to x = 10y. You used that knowledge to convert between exponential and logarithmic expressions. You will now explore how the graph of y = 10x compares to the graph of x = 10y.

 

Try This 1

1. Complete tables of values like the following.
   
   

   y = 10x
   x	y
   −2
   −1
   0
   1

   
   
   

   x = 10y
   x	y
   	−2
   	−1
   	0
   	1

2. How are the values of x and y related in the two functions?

3. Draw the graph of y = x. On the same Cartesian plane, draw the graphs of y = 10x and x = 10y using your tables of values from question 1.
4. Describe a possible method for sketching the graph of x = 10y from the graph of y = 10x.
5. Identify the following characteristics of your graphs of y = 10x and x = 10y.
   
   

   Characteristics	y = 10x	x = 10y
   Domain
   Range
   x-intercept
   y-intercept
   End Behaviour

Save your responses in your course folder.

 

Share 1

 

With a partner or group, discuss the following based on your graphs created in Try This 1: What is the relationship between the characteristics of the function y = 10x and the characteristics of the function x = 10y?

 

If required, place a summary of your discussion in your course folder.