Answer:
option B) f(x) = x³ - 3
Step-by-step explanation:
we know that
If the function represent the set of ordered pairs, then the ordered pairs, must be satisfy the function
Verify each function
case A) f(x) = -2x
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
[tex]f(2)=-2(2)=-4[/tex]
[tex]-4\neq 5[/tex]
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs
case B) f(x) = x³ - 3
Verify (1,-2)
For x=-1 ---> [tex]f(1)=1^{3}-3=-2[/tex] ---> is ok
Verify (2,5)
For x=-2 ---> [tex]f(2)=2^{3}-3=5[/tex] ---> is ok
Verify (3,24)
For x=3 ---> [tex]f(3)=3^{3}-3=24[/tex] ---> is ok
Verify (4,61)
For x=4 ---> [tex]f(4)=4^{3}-3=61[/tex] ---> is ok
so
the ordered pairs satisfy the function
therefore
The function represent the set of ordered pairs
case C) f(x) = x² - 3
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
[tex]f(2)=2^2-3=1[/tex]
[tex]1\neq 5[/tex]
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs
case D) f(x) = 5x² - 7
verify the ordered pair (2,5)
For x=2
substitute the value of x in the function and then compare the result with the y-coordinate of the ordered pair
[tex]f(2)=5(2)^2-7=13[/tex]
[tex]13\neq 5[/tex]
the ordered pair not satisfy the function
so
The function nor represent the set of the ordered pairs
