McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 6 Page 265

Start by making a table of values.

Domain: {all real numbers}
Range: {f(x) | f(x)<0}

Practice makes perfect

Let's begin by graphing the function. Then we will state its domain and range.

Graphing the Function

To graph the given exponential function, we will first make a table of values.
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.

Determining the Domain and Range

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 }