Question

Which could be the function graphed below?

Answer 1

Given graph represents function.

Explanation:

We have been given a graph. Now we need to find if the given graph represents function or not.

To check if any graph represents function or not, we apply vertical line test. That means if there exists any vertical line that crosses the given graph more than once then the given graph is not a function.

Now if you draw vertical lines then you won't find any such vertical line which crosses graph more than once.

Hence given graph represents function.

Answer 2

`f(x=√(x)-2`.

Explanation:

We have been given graph of a function. We are supposed to find the function formula.

Upon looking at our given function, we can see that it is transformed form of a square root function.

We know that square root parent function is in form
`f(x)=√(x)`.

We can see that our given graph is shifted down along y-axis. The rule for shifting a graph down along y-axis is:
`f(x)\rightarrow f(x)-a`, where graph of
`f(x)` is shifted down by a units.

So our function will be in form
`f(x=√(x)-a`.

From our attached file, we can see that value of 'a' is 2.

Therefore, our required function would be
`f(x=√(x)-2`.