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=-√(x-1)+5`

To find:

The end behaviour of the function.

Step-by-step explanation:

It is given that,

`y=-√(x-1)+5`

And, the graph of the above function is,

That implies,

From the graph,

As x tends to 1,

`\begin{gathered} y=-√(1-1)+5 \\ y=-√(0)+5 \\ y=5 \end{gathered}`

Also,

`\begin{gathered} y=-√(x-1)+5 \\ \Rightarrow y-5=-√(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}`