Question

For the function f shown in the graph below, what is the local minimum? Question

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?

Select all correct answers.

Select all that apply:

{(4,9),(0,−2),(0,2),(5,4)}
{(5,−5),(5,−4),(7,−2),(3,8)}
{(4,3),(8,0),(5,2),(−5,0)}
{(6,9),(9,−4),(6,1),(−5,11)}
{(4,12),(2,6),(−5,6),(3,−2)}

Answer 1

For the function shown in the graph, the local minimum is at the point (2, -3).

To determine whether a relation is a function, we need to check whether each input (x-value) in the relation is associated with exactly one output (y-value). One way to do this is to check if there are any repeated x-values with different y-values.

Out of the given answer choices:

{(4,9),(0,−2),(0,2),(5,4)} is not a function since there are two different y-values associated with the x-value 0.

{(5,−5),(5,−4),(7,−2),(3,8)} is not a function since there are two different y-values associated with the x-value 5.

{(4,3),(8,0),(5,2),(−5,0)} is a function since there are no repeated x-values.

{(6,9),(9,−4),(6,1),(−5,11)} is not a function since there are two different y-values associated with the x-value 6.

{(4,12),(2,6),(−5,6),(3,−2)} is a function since there are no repeated x-values.

Therefore, the answer choices that represent a function are:

{(4,3),(8,0),(5,2),(−5,0)}

and

{(4,12),(2,6),(−5,6),(3,−2)}

So the correct options are:

{(4,3),(8,0),(5,2),(−5,0)}

and

{(4,12),(2,6),(−5,6),(3,−2)}