Domain: {all real numbers} Range: {f(x) | f(x) >2}
Let's start 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^(x-3)+2Because the base of the function is greater than 1, we know that this is an exponential growth function. To do so, we will start by making a table of values.
x
3^(x-3)+2
y=3^(x-3)+2
1
3^(1-3)+2
2.111...
2
3^(2-3)+2
2.333...
3
3^(3-3)+2
3
4
3^(4-3)+2
5
5
3^(5-3)+2
11
The ordered pairs ( 1, 2.111), ( 2, 2.333), ( 3, 3), ( 4, 5) and ( 5, 11) all lie on the 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=2, so the range is all real numbers that are greater than 2.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >2 }
