Consider the given function.

which graph represents the given function?

C

Step-by-step explanation:

First take a look at the value of if :

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 is not equal to 5 for :

For answer A it is correct, i.e.    for  

For answer B, we can see that  for so we can eliminate that answer.

For answer C it is correct, i.e.    for  

For answer D, we can see that  for so we can eliminate that answer.

Now we can take a look at the function equation at :

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 so that does not match the definition of

On the graph C we can see that and that does match the definition of .

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)