Question

Shown is the graph of the function y = -√x-1+5.10Determine the end behavior of the function.10

Answer 1

Given

The function,

$y=-\sqrt{x-1}+5$

To find:

The end behaviour of the function.

Explanation:

It is given that,

$y=-\sqrt{x-1}+5$

And, the graph of the above function is,

That implies,

From the graph,

As x tends to 1,

$\begin{gathered} y=-\sqrt{1-1}+5 \\ y=-\sqrt{0}+5 \\ y=5 \end{gathered}$

Also,

$\begin{gathered} y=-\sqrt{x-1}+5 \\ \Rightarrow y-5=-\sqrt{x-1} \\ \Rightarrow(y-5)^2=x-1 \end{gathered}$

Then,

As x tends to infinity,

$\begin{gathered} (y-5)^2=\infty \\ y-5=\infty \\ y\rightarrow\infty \end{gathered}$

Hence, the answer is option C),

$\begin{gathered} x\rightarrow\infty,\text{ }y\rightarrow\infty \\ x\rightarrow1,\text{ }y\rightarrow5 \end{gathered}$