Question

Graph the given functions on a common screen. How are these graphs related?

y = 3^x,     y = 10^x,      y = (1/3)^x,          y = (1/10)^x

Answer 1

Step 1:

General form of exponential functions

When , increasing.

, decreasing.

is increasing.

is increasing.

 is decreasing.

 is increasing.

Step 2:

To graph the functions find the coordinate pairs.

-1		(-1, 0.33)
1		(1, 3)

 

-1		(-1, 0.1)
0.5		(0.5, 3.16)

 

-1		(-1, 3)
1		(1, 0.33)

 

-0.5		(-0.5, 3.16)
1		(1, 0.1)

 

Comments

Contd...

Draw the coordinate plane.

Plot the points found in the table and connect the curves.

Graph:

Observe the all graphs are passes through .

The base of the exponential function gets larger, the exponential function grows more rapidly[for ].

Solution:

The base of the exponential function gets larger, the exponential function grows more rapidly[for )]