Question

Write a function to represent the set of ordered pairs.

Answer 1

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

$f(2)=-2(2)=-4$

$-4\neq 5$

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 ---> $f(1)=1^{3}-3=-2$ ---> is ok

Verify (2,5)

For x=-2 ---> $f(2)=2^{3}-3=5$ ---> is ok

Verify (3,24)

For x=3 ---> $f(3)=3^{3}-3=24$ ---> is ok

Verify (4,61)

For x=4 ---> $f(4)=4^{3}-3=61$ ---> 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

$f(2)=2^2-3=1$

$1\neq 5$

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

$f(2)=5(2)^2-7=13$

$13\neq 5$

the ordered pair not satisfy the function

so

The function nor represent the set of the ordered pairs