Study Guide and Review
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Start by making a table of values.
Domain: {all real numbers}
Range: {f(x) | f(x)<0}
Let's begin by graphing the function. Then we will state its domain and range.
x | -5(2)^x | y=-5(2)^x |
---|---|---|
- 3 | -5(2)^(- 3) | -0.625 |
- 2 | -5(2)^(- 2) | -1.25 |
- 1 | -5(2)^(- 1) | -2.5 |
0 | -5(2)^0 | -5 |
1 | -5(2)^1 | -10 |
2 | -5(2)^2 | -20 |
All of the ordered pairs ( - 3, -0.625), ( - 2, -1.25), ( - 1, -2.5), ( 0, -5), ( 1, -10), and ( 2, -20) belong to the graph of our function, so now we need to plot and connect these points with a smooth curve.
Unless a restriction is specifically stated, the domain of any exponential function is all real numbers. The graph of our function is below the x -axis, so the range is all real numbers that are less than 0. Domain:& { all real numbers } Range:& {f(x) | f(x) <0 }