# How do you graph y=-2^x?

May 14, 2018

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Create a data table to graph the exponential function : color(red)(y=-2^x

#### Explanation:

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color(green)("Step 1 :"

Create a data table:

Closely examine the values for $x$ and $y$

No value of $x$ makes $y$ zero.

So, the graph gets closer and closer to the x-axis but never touches the x-axis.

Hence, color(brown)(y=0 is the horizontal asymptote.

color(green)("Step 2 :"

Using the data table, graph the function $y = f \left(x\right) = - {2}^{x}$

For easy comprehension, graph the exponential function $y = f \left(x\right) = {2}^{x}$, it's parent function.

Compare both the graphs to understand the behavior of the given exponential function $y = f \left(x\right) = - {2}^{x}$

The graph of $y = f \left(x\right) = - {2}^{x}$ is reflected about the x-axis when the sign of $f \left(x\right)$ is negative.