To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:
4x^2 - 9x + 9 = 0
We can use the quadratic formula to find the roots:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = -9, and c = 9, so:
x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)
x = (9 ± sqrt(81 - 144)) / 8
x = (9 ± sqrt(-63)) / 8
Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.