Question

The function f(x)=5^(x-1) is shown on the coordinate plane. Select from the drop down menus to correctly describe the end behavior of f(x)

Answer 1

Answer: The end behavior of the given function is,

`f(x)\rightarrow 0` as
`x\rightarrow -\infty`

And,
`f(x)\rightarrow \infty` as
`x\rightarrow \infty`

Explanation:

Since, by the property of the graph of the exponential function,

If an exponential function is,
`f(x) = ab^x`

If b >1 ( increasing function ) then its end behavior is,

`f(x)\rightarrow 0` as
`x\rightarrow -\infty`

And,
`f(x)\rightarrow \infty` as
`x\rightarrow \infty`

While b < 1 ( decreasing function, then its end behavior is,

`f(x)\rightarrow \infty` as
`x\rightarrow -\infty`

And,
`f(x)\rightarrow 0` as
`x\rightarrow \infty`

Here, given function is,
`f(x)=5^(x-1)`

Since 5 > 1

Therefore, the end behavior of the given function is,

`f(x)\rightarrow 0` as
`x\rightarrow -\infty`

And,
`f(x)\rightarrow \infty` as
`x\rightarrow \infty`