Consider the function f(x)=-16x2 +64x+4.
a) Determine the domain and range of the function.
b) Suppose this function represents the height, in feet, of a football kicked into the air as a function of time, in seconds. What are the domain and range in this case?
c) Explain why the domain and range are different in parts a) and b).
+23245 Part a:
Domain: set of all possible real numbers: -∞ < x < ∞
Range: the set of all real numbers less than or equal to 68: -∞ < x < 68
Part b:
Domain: 0 ≤ x ≤ 4
Range: 0 ≤ y ≤ 68
Part c:
The graph is a model of the time that the ball is in the air and the height of the ball.
x represents time; it can't be less than 0, nor can it be greater than the time that the ball returns to earth (the bouncing after that is not part of this equation).
y represents height; it can't be less than 0, for the ball is not kicked out of a hole nor is it kicked into a hole.
These restrictions weren't put into the equation.
+23245 Part a:
Domain: set of all possible real numbers: -∞ < x < ∞
Range: the set of all real numbers less than or equal to 68: -∞ < x < 68
Part b:
Domain: 0 ≤ x ≤ 4
Range: 0 ≤ y ≤ 68
Part c:
The graph is a model of the time that the ball is in the air and the height of the ball.
x represents time; it can't be less than 0, nor can it be greater than the time that the ball returns to earth (the bouncing after that is not part of this equation).
y represents height; it can't be less than 0, for the ball is not kicked out of a hole nor is it kicked into a hole.
These restrictions weren't put into the equation.
