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 the x-coordinate of the point, we need to solve the equation f(x) = 0:
x^3 - 9 = 0
Adding 9 on both sides, we get:
x^3 = 9
Taking the cube root of both sides, we find:
x = ∛9
Since 9 is not a perfect cube, we cannot simplify the radical any further. Therefore, the exact value of x is ∛9.
Now, to determine the y-coordinate of the point, we substitute the value of x into the original equation:
f(∛9) = (∛9)^3 - 9
Simplifying, we have:
f(∛9) = 9 - 9
f(∛9) = 0
Therefore, the point (x, y) = (∛9, 0) is on the graph of f(x) = x^3 - 9.
However, none of the given answer choices include (∛9, 0), so none of the options provided correctly justify the answer.