Domain: {all real numbers} Range: {f(x) | f(x) >- 3}
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)=2( 3/4)^(x+1)-3Because the base of the function is greater than 0, but less than 1, we know that this is an exponential decay function. To do so, we will start by making a table of values.
x
2(3/4)^(x+1)-3
y=2(3/4)^(x+1)-3
- 4
2(3/4)^(- 4+1)-3
1.741
- 3
2(3/4)^(- 3+1)-3
0.556
- 2
2(3/4)^(- 2+1)-3
- 0.333
- 1
2(3/4)^(- 1+1)-3
- 1
0
2(3/4)^(0+1)-3
- 1.5
1
2(3/4)^(1+1)-3
- 1.875
2
2(3/4)^(2+1)-3
- 2.156
The ordered pairs ( - 4, 1.741), ( - 3, 0.556), ( - 2, - 0.333), ( - 1, - 1), ( 0, - 1.5), ( 1, -1.875), and ( 2, - 2.156) 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=- 3, so the range is all real numbers that are greater than - 3.
Domain:& { all real numbers }
Range:& {f(x) | f(x) >- 3 }
