3. Exponential Functions
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Make a table to find ordered pairs. Then, plot and connect the points with a smooth curve.
Graph:
Domain: All real numbers
Range: y< 0
Comparison to the Parent Function: See solution.
Let's graph and describe the domain and range of the given function first. Then we will compare the graph to the graph of the parent function.
To graph the given exponential function, we will first make a table of values.
| x | - 2(4)^x | f(x)=- 2(4)^x |
|---|---|---|
| - 2 | - 2(4)^(- 2) | - 0.125 |
| 0 | - 2(4)^0 | - 2 |
| 1 | - 2(4)^1 | - 8 |
| 2 | - 2(4)^2 | - 32 |
Let's now plot and connect the points ( - 2, - 0.125), ( 0, - 2), ( 1, - 8), and ( 2, - 32) with a smooth curve.
We can see in the graph that the range is all real numbers less than zero. The domain of exponential functions is all real numbers. Domain:& All real numbers Range:& y< 0
The parent function is g(x)=4^x. Let's graph it on the same coordinate plane. To do it, we will make a table of values first.
| x | 4^x | g(x)=4^x |
|---|---|---|
| - 2 | 4^(- 2) | 0.0625 |
| 0 | 4^0 | 1 |
| 1 | 4^1 | 4 |
| 2 | 4^2 | 16 |
Let's now plot and connect the points ( - 2, 0.0625), ( 0, 1), ( 1, 4), and ( 2, 16) with a smooth curve.
We can tell that the graph of f is a vertical stretch by a factor of 2, and a reflection in the x-axis of the graph of g. The y-intercept of the graph of f, - 2, is under the y-intercept of the graph of the parent function, 1.