Sketch the graph of the exponential y= 2^x _ 5 ?

To sketch the graph of the exponential function y = 2^x - 5, we can start by plotting a few key points and then connecting them to create the graph.

Key points:
When x = 0, y = 2^0 - 5 = 1 - 5 = -4
When x = 1, y = 2^1 - 5 = 2 - 5 = -3
When x = -1, y = 2^-1 - 5 = 1/2 - 5 = -4.5

Plotting these points and connecting them with a smooth curve, we get the following graph:

The graph of y = 2^x - 5 is a decreasing exponential function that approaches the x-axis but never touches it. The graph is shifted down by 5 units compared to the standard exponential function y = 2^x.

Step 1: Create a table of values

Choose some input values for x and calculate the corresponding output values for y using the given equation:

| x | y = 2^(x-5) |
|---|---|
| -2 | 0.03125 |
| -1 | 0.0625 |
| 0 | 0.125 |
| 1 | 0.25 |
| 2 | 0.5 |
| 3 | 1 |

Step 2: Plot the points

Use the table of values to plot the points on the coordinate plane.

Step 3: Draw the curve

Connect the points with a smooth, rising curve. The curve should start near the origin (0,0) and approach but never touch the x-axis.

Step 4: Label the axes

Label the x-axis as "x" and the y-axis as "y".

Final Graph:

The graph of y = 2^(x-5) is an exponential curve that rises rapidly as x increases. It approaches but never touches the x-axis. The graph should look similar to the following:

[Image of the exponential graph y= 2^x _ 5]

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