Domain: { all real numbers } Range: { f(x) | f(x) > 0 }
Practice makes perfect
We want to draw a graph of the given exponential function.
f(x)= 2^x
Because the base of the function is greater than 1, we know that this is an exponential growth function. To draw the graph, we will start by making a table of values.
x
2^x
f(x)=2^x
- 3
2^(- 3)
0.125
- 2
2^(- 2)
0.25
- 1
2^(- 1)
0.5
0
2^0
1
1
2^1
2
2
2^2
4
The ordered pairs ( - 3, 0.125), ( - 2, 0.25), ( - 1, 0.5), ( 0, 1), ( 1, 2), and ( 2, 4) all lie on the function. Now, we will plot and connect these points with a smooth curve.
We can see in the graph that the range is all real numbers greater than 0. The domain of exponential functions is all real numbers.
Domain:& {all real numbers}
Range:& {f(x) | f(x)>0}
