Domain: {all real numbers} Range: {f(x) | f(x)>-6}
Practice makes perfect
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( 4)^x-6Because 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(4)^x-6
y=3(4)^x-6
- 2
3(4)^(- 2)-6
- 5.8125
- 1
3(4)^(- 1)-6
-5.25
0
3(4)^0-6
-3
1
3(4)^1-6
6
2
3(4)^2-6
42
All of the ordered pairs ( - 2, - 5.8125), ( - 1, -5.25), ( 0, -3), ( 1, 6), and ( 2, 42) 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= -6, so the range is all real numbers that are greater than -6.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >-6 }
