Question

When an object is dropped from above the ground the equation Y= 16x ^2 represents the number of feet y that the object falls in X seconds until it hits the ground a student claims that Y is not a function of X because X is squared is the student correct

Answer 1

The student is not correct. Y = 16x^2 is a function of X.

A function is a mathematical relationship between two variables, where each value of the independent variable (in this case, X) corresponds to exactly one value of the dependent variable (in this case, Y). The equation Y = 16x^2 satisfies this definition.

The fact that X is squared in the equation does not mean that it is not a function of X. In this case, Y is a function of X because for each value of X, there is a unique value of Y determined by the equation Y = 16x^2.

This equation represent the distance an object falls (Y) in a certain amount of time (X) assuming that the only force acting on the object is gravity, and the acceleration due to gravity is constant (approximately 9.8 m/s^2 or 32 ft/s^2). The equation Y = 16x^2 is known as the equation of motion under gravity.