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^xBecause the base of our function is greater than 1, we know that it is an exponential growth function. In order to draw it, let's start by making a table of values.
x
3^x
y=3^x
- 3
3^(- 3)
0.037...
- 2
3^(- 2)
0.111...
- 1
3^(- 1)
0.333...
0
3^0
1
1
3^1
3
2
3^2
9
All of the ordered pairs ( - 3, 0.037), ( - 2, 0.111), ( - 1, 0.333), ( 0, 1), ( 1, 3), and ( 2, 9) belong to the graph of our function, so now we need to 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 x -axis, so the range is all real numbers that are greater than 0.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >0 }
