choose an ordered pair that represents a solution to each function
f(x)= -x^3 -9
A) (-2, -17)
B) (-2, 1)
C) (-2, 8)
D) (-2, 4)
E) (-2, -1)
F) (-2, 9)
Justify your answer
To determine if an ordered pair represents a solution to the function, we substitute the x-coordinate into the function and see if the result matches the y-coordinate.
Let's try each option:
A) (-2, -17)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate does not match, so (-2, -17) is not a solution to the function.
B) (-2, 1)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate does not match, so (-2, 1) is not a solution to the function.
C) (-2, 8)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate does not match, so (-2, 8) is not a solution to the function.
D) (-2, 4)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate does not match, so (-2, 4) is not a solution to the function.
E) (-2, -1)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate matches, so (-2, -1) is a solution to the function.
F) (-2, 9)
Substituting -2 into the function, we get:
f(-2) = -(-2)^3 - 9
f(-2) = -(-8) - 9
f(-2) = 8 - 9
f(-2) = -1
The y-coordinate does not match, so (-2, 9) is not a solution to the function.
The ordered pair that represents a solution to the function is (-2, -1) from option E.