Answer:

 

y = 3x is a linear function and y = 3x is an exponential function. 

 

Linear functions have a constant rate of change while exponential functions have varying rates of change. 

 

The linear equation, y = 3x has a constant rate of change of 3 (as x increases by 1, y increases by 3). 

 

The exponential function has a varying rate of change. The rates of change depend upon the value of x and the function.

 

The domain and range of y = 3x is domain {x:  x Î Â }(all real numbers) and range   { y:  y Î Â }(all real numbers).

 

The domain and range of   y = 3x is domain {x:  x Î Â } (all real numbers) and range {y:  y > 0}.

 

x

3x

3x

-6

-18

0.00137

-5

-15

0.00412

-4

-12

0.01235

-3

-9

0.03704

-2

-6

0.11111

-1

-3

0.33333

0

0

1

1

3

3

2

6

9

3

9

27

4

12

81

5

15

243

6

18

729

 

 

 

 

                       

 

 

 

 

 

 

 

 

 

 

 

 

TEACHER NOTES:

Students will identify y = 3x as a linear equation and one that has a constant growth of 3, with each increase of x by 1, y will increase by 3.  y = 3x is a straight line.  y = 3x is exponential, as x increases by 1, y will triple. With each change in the x value the y value will change by 3 times the previous y value.  This will not be a straight-line graph.  As x becomes negative (moving right to left) for the first equation it will continue to decrease (since moving from right to left) by 3.  y = 3x will have a y value that will get closer and closer to (or approach) zero, but not equal zero.