Question

Consider the given function.

Which graph represents the given function?

Answer 1

C

Explanation:

First take a look at the value of
`f` if
`x<-2`:

From the definition of the function we can see that that value is 5.

Now take a look at the graph and eliminate graphs where
`f` is not equal to 5 for
`x<-2`:

For answer A it is correct, i.e.
`f=5` for
`x<-2`

For answer B, we can see that
`f=-3` for
`x<-2` so we can eliminate that answer.

For answer C it is correct, i.e.
`f=5` for
`x<-2`

For answer D, we can see that
`f=-3` for
`x<-2` so we can eliminate that answer.

Now we can take a look at the function equation at
`x=-2`:

From the definition of the function we can see that that value is 3.

We have to check A and C:

On the graph in A we can see that
`f(-2) = 5` so that does not match the definition of
`f`

On the graph C we can see that
`f(-2)=3` and that does match the definition of
`f`.

So, since we have eliminated A, B and D, the correct answer is C

(You can further check for C if it matches the function definition if you wish)