Let's begin by graphing the function. Then we will state its domain and range.
Graphing the Function
We want to draw a graph of the given exponential function.
f(x)=3/5( 2/3 )^(x-2)+3
Because the base of our function is less than 1, we know that it is an exponential decay function. Let's start by making a table of values.
x
3/5(2/3)^(x-2)+3
y=3/5(2/3)^(x-2)+3
- 3
3/5(2/3)^(- 3-2)+3
7.556 ...
- 2
3/5(2/3)^(- 2-2)+3
6.0375
- 1
3/5(2/3)^(- 1-2)+3
5.025
0
3/5(2/3)^(0-2)+3
4.35
1
3/5(2/3)^(1-2)+3
3.9
2
3/5(2/3 )^(2-2)+3
3.6
All of the ordered pairs ( - 3, 7.556), ( - 2, 6.0375), ( - 1, 5.025), ( 0, 4.35), ( 1, 3.9) and ( 2, 3.6) belong to the graph of our function. Now, we will plot and connect these points with a smooth curve.
Determining the Domain and Range
Unless a restriction is specifically stated, the domain of any exponential function is all real numbers. The graph of our function is above the line y=3, so the range is all real numbers that are greater than 3.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >3 }
