Question

Consider the given function.

Which graph represents the given function?

Answer 1

Answer:

C

Step-by-step 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)