Consider statement A,
f(x) can be written as g(x) − 9, ∴ the graph of f(x) will be 9 units below the graph of g(x).
∴ Statement A is not true.
Consider statement B,
Zeroes i.e. roots of the given function are 3/2 and 4, ∴ the sum of the zeroes = 1.5 + 4 = 5.5
∴ Statement B is also not true.
Consider statement C:
Substituting the values of x, y and m in the equation y = mx + c, we get,
4 = −3 × 6 + c
∴ yintercept = c = 22
∴ Statement C is also not true.
Consider statement D,
Substituting the values of x in the function from the domain, the values of f(x) that we get, represent the range.
For, x = −4, f(x) = 12 × (−4)^{2} + 2 = 194
Similarly, for x = 0, f(x) = 2 and for x = 3, f(x) = 110
∴ Statement D is true.
Consider statement E,
Nature of graphs of both the functions f(x) and g(x) is same (similar to x^{2}), but the coefficient of f(x) is more than the coefficient of g(x), therefore graph of f(x) will be narrow as compared to graph of g(x).
∴ Statement E is true.
Consider statement F,
The xintercept represents the amount of time it takes for all of the sand to pass to the bottom of the hourglass (and not the speed).
∴ Statement F is not true.
Hence, option 3.
