(-2,-8)is a point of f(x)=x³, then point of f(x)=(x+5)³-3 is*(3,-5)(3,-11)(-8,-11)(-8,-5)
Question
(-2,-8)is a point of f(x)=x³, then point of f(x)=(x+5)³-3 is*(3,-5)(3,-11)(-8,-11)(-8,-5)
Solution
The given point (-2,-8) is on the graph of the function f(x) = x³. This means that when x = -2, f(x) = (-2)³ = -8.
The function f(x) = (x+5)³ - 3 is a transformation of the function f(x) = x³. Specifically, it is a shift to the left by 5 units and down by 3 units.
So, to find the corresponding point on the graph of f(x) = (x+5)³ - 3, we need to shift the x-coordinate of the given point to the right by 5 units and the y-coordinate down by 3 units.
Shifting the x-coordinate of -2 to the right by 5 units gives -2 + 5 = 3.
Shifting the y-coordinate of -8 down by 3 units gives -8 - 3 = -11.
So, the corresponding point on the graph of f(x) = (x+5)³ - 3 is (3, -11). Therefore, the correct answer is (3, -11).
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