To construct a table of values for the given exponential function \(f(x) = 2^{x} + 4\) for \(x = -2, -1, 0, 1, 2\), you can calculate the values as follows:
Next, you can sketch the graph of this exponential function on a coordinate plane using these values. The graph will be an increasing curve that approaches a horizontal asymptote.
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Answer:
To construct a table of values for the given exponential function \(f(x) = 2^{x} + 4\) for \(x = -2, -1, 0, 1, 2\), you can calculate the values as follows:
1. For \(x = -2\):
\(f(-2) = 2^{-2} + 4 = \frac{1}{4} + 4 = \frac{17}{4}\)
2. For \(x = -1\):
\(f(-1) = 2^{-1} + 4 = \frac{1}{2} + 4 = \frac{9}{2}\)
3. For \(x = 0\):
\(f(0) = 2^{0} + 4 = 1 + 4 = 5\)
4. For \(x = 1\):
\(f(1) = 2^{1} + 4 = 2 + 4 = 6\)
5. For \(x = 2\):
\(f(2) = 2^{2} + 4 = 4 + 4 = 8\)
Now, you can create the table of values:
| x | f(x) |
|:-----:|:-------:|
| -2 | 17/4 |
| -1 | 9/2 |
| 0 | 5 |
| 1 | 6 |
| 2 | 8 |
Next, you can sketch the graph of this exponential function on a coordinate plane using these values. The graph will be an increasing curve that approaches a horizontal asymptote.