Let's now plot and connect the points ( - 2, 0.0078), ( 0, 0.5), ( 1, 4), and ( 2, 32) with a smooth curve.
We can see in the graph that the range is all real numbersgreater than zero. The domain of exponential functions is all real numbers.
Domain:& All real numbers
Range:& y>0
Comparing the Graph to the Parent Function
The parent function is g(x)=8^x. Let's graph it on the same coordinate plane. To do it, we will make a table of values first.
x
8^x
g(x)=8^x
- 2
8^(- 2)
≈ 0.016
0
8^0
1
1
8^1
8
1.5
8^(1.5)
≈ 23
Let's now plot and connect the points ( - 2, 0.016), ( 0, 1), ( 1, 8), and ( 1.5, 23) with a smooth curve.
We can tell that the graph of f is a vertical shrink by a factor of 12 of the graph of g. The y-intercept of the graph of f, 0.5, is under the y-intercept of the graph of the parent function, 1.
