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^(2x)+5Because the base of our function is greater than 1, we know that it is an exponential growth function. Let's start by making a table of values.
x
3^(2x)+5
y=3^(2x)+5
- 2
3^(2( - 2))+5
5.012...
- 1
3^(2( - 1))+5
5.111 ...
0
3^(2( 0))+5
6
1
3^(2( 1))+5
14
2
3^(2( 2))+5
86
All of the ordered pairs ( - 2, 5.012), ( - 1, 5.111), ( 0, 6), ( 1, 14), and ( 2, 86) 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=5, so the range is all real numbers that are greater than 5.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >5 }
