Question

Determine the asymptote and find the x & y values

Answer 1

The horizontal asymptote of
`\(f(x)=((1)/(5))^(x+3)\)` is y=0. To graph it, start with
`\(y=((1)/(5))^x\)`, shift left by 3, and scale down by
`\((1)/(5)\)`.

Sure, I can help you with this. The horizontal asymptote of the graph of
`$f(x)=((1)/(5))^(x+3)$` is the line y=0. This is because as x approaches positive or negative infinity, the value of
`$((1)/(5))^(x+3)$` approaches zero.

To graph the function, you can first use the fact that the graph of

`$y=((1)/(5))^x$` passes through the points (0,1) and (1,-1). To get the graph of f(x), you can then shift the graph of
`$y=((1)/(5))^x$` three units to the left and scale it down by a factor of
`(1)/(5)`.

Here are the steps for graphing the function:

1. Draw the graph of
`$y=((1)/(5))^x$`. Remember that the graph passes through the points (0,1) and (1,-1).

2. Shift the graph of $y=(\frac{1}{5})^x$ three units to the left. This will give you the graph of
`$y=((1)/(5))^x+3$`.

3. Scale the graph of
`$y=((1)/(5))^x+3$` down by a factor of $\frac{1}{5}$. This will give you the graph of
`f(x)=((1)/(5))^(x+3)$`.

Once you have the graph, you can see that the horizontal asymptote is the line y=0.

Here are some additional things to note about the graph of $f(x)$:

* The domain of the function is all real numbers.

* The range of the function is all positive real numbers less than

`$(1)/(5)$`.

* The function is decreasing for all real numbers.

* The y-intercept of the graph is the point
`$\left(-3,(1)/(5)\right)$.`

I hope this helps! Let me know if you have any other questions.