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 $x\rightarrow \infty$

Step-by-step 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 $x\rightarrow \infty$