Question

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

Answer 1

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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(x)=-2^x`

For easy comprehension, graph the exponential function `y=f(x)=2^x`, it's parent function.

Compare both the graphs to understand the behavior of the given exponential function `y=f(x)=-2^x`

The graph of `y =f(x)=-2^x` is reflected about the x-axis when the sign of `f(x)` is negative.