Chapter Test
Sign In
Start by making a table of values.
Graph:
Comparison: The function f(x) is a vertical stretch of the function g(x) of a factor of 2.
Domain of f(x): All real numbers
Range of f(x): y>0
We are asked to graph f(x)=2(6)^x, compare the graph to the graph of g(x)=6^x, and describe the domain and range of f. We will do this one at a time.
Because the base of the function is greater than 1, we know that this is an exponential growth function. To graph the function, we will start by making a table of values.
| x | 2(6)^x | y=2(6)^x |
|---|---|---|
| - 2 | 2(6)^(- 2) | 0.055... |
| - 1 | 2(6)^(- 1) | 0.333... |
| 0 | 2(6)^0 | 2 |
| 1 | 2(6)^1 | 12 |
The ordered pairs ( - 2, 0.055), ( - 1, 0.333), ( 0, 2), and ( 1, 12) all lie on the graph of the function. We will plot and connect these points with a smooth curve.
Now we are asked to compare the graph of f(x) to the graph of g(x)=6^x. Let's draw them!
Notice that the graph of f(x) is a vertical stretch of the function g(x) by a factor of 2.
Now we will determine the domain and the range of f(x). Since the domain of all exponential functions is all real numbers, the domain of f(x) is all real numbers. Moreover, from the graph of f(x) we can see that the range of f(x) is y>0.