the function ( f(x) ) is given by the set of ordered pairs. \n ( { (1,0), (-10,2), (0,6), (3,17), (-2,-1) }…

the function ( f(x) ) is given by the set of ordered pairs. \n ( { (1,0), (-10,2), (0,6), (3,17), (-2,-1) } ) \n which equation is true? \n ( \bigcirc f(-10)=1 ) \n ( \bigcirc f(2)=-10 ) \n ( \bigcirc f(0)=6 ) \n ( \bigcirc f(1)=-10 )

the function ( f(x) ) is given by the set of ordered pairs. \n ( { (1,0), (-10,2), (0,6), (3,17), (-2,-1) } ) \n which equation is true? \n ( \bigcirc f(-10)=1 ) \n ( \bigcirc f(2)=-10 ) \n ( \bigcirc f(0)=6 ) \n ( \bigcirc f(1)=-10 )

Answer

Explanation:

Step1: Recall the definition of a function

In a function (f(x)) given as a set of ordered pairs ((x,y)), (y = f(x)). That is, for an ordered pair ((a,b)), when (x=a), (f(a)=b).

Step2: Check each option

  • For the option (f(-10) = 1): Looking at the set of ordered pairs ({(1,0),(-10,2),(0,6),(3,17),(-2,-1)}), when (x = - 10), (y=f(-10)=2\neq1).
  • For the option (f(2)=-10): The set of ordered pairs ({(1,0),(-10,2),(0,6),(3,17),(-2,-1)}) does not have an ordered pair with (x = 2).
  • For the option (f(0)=6): Since there is an ordered pair ((0,6)) in the set ({(1,0),(-10,2),(0,6),(3,17),(-2,-1)}), by the definition of (y = f(x)) (where (x = 0) and (y=6)), we have (f(0)=6).
  • For the option (f(1)=-10): Looking at the set of ordered pairs ({(1,0),(-10,2),(0,6),(3,17),(-2,-1)}), when (x = 1), (y=f(1)=0\neq - 10).

Answer:

(f(0)=6)