How do you graph #f(x)=3^(x - 2)#?

1 Answer
Sridhar V.
May 4, 2018

#" "#
Please read the explanation.

Explanation:

#" "#
Given the exponential function: #color(red)(f(x)=3^(x-2)#

Before graphing this function, create a data table:

The table should contain values for #color(red)(x#, corresponding values for #color(red)(y=3^x) and color(red)(y=3^(x-2)#

We include the base function: #color(red)(y=3^x#, since it provides an opportunity to examine the behavior of both the graphs by comparing them.

The table shows #color(red)x# and the corresponding #color(red)(y# values:

enter image source here

Construct both the graphs:

#color(green)"Graph 1:"#

#color(blue)("Graph of "y = f(x) = 3^x#

enter image source here

Domain : #(-oo, oo)#

Range : #(0, oo)#

y-intercept : #(0,1)#

Horizontal Asymptote :#y=0#

#color(green)"Graph 2:"#

#color(blue)("Graph of "y = f(x) = 3^(x-2#

enter image source here

Domain : #(-oo, oo)#

Range : #(0, oo)#

y-intercept : #(0,1/0)#

Horizontal Asymptote :#y=0#

#color(green)"Graph 3:"#

#color(blue)("Graph of "y = f(x) = 3^(x) and y = f(x) = 3^(x-2)#

Compare the behavior of both graphs:

enter image source here

Translation is horizontal for #y = f(x) = 3^(x-2)# by #color(red)(2# units.

Hope it helps.

Related questions
See all questions in Linear, Exponential, and Quadratic Models
Impact of this question
12714 views around the world
You can reuse this answer
Creative Commons License