Question

Compare the functions shown below:


Which function has the most x-intercepts?

Answer 1

Okay, x-intercepts are the points on the graph where y = 0 i.e. where the graph cuts the x-axis. The graph of g(x) has three that we can see but is restricted to 0 < x < 2Pi which means it only has two. The graph of f(x) however, is unrestricted and we can see four x-intercepts so the question is whether it is f(x) or h(x) with the most intercepts.

Now as y = h(x) and h(x) = 2x^3 - 2x^2 - 3x +2; when y = 0 then

2x^3 - 2x^2 - 3x +2 = 0

Which is extremely difficult to factorise and work with. So what is easier to do is remember that a cubic function should have two turning points. If this occurs close to the x-axis, there will be three roots (x-intercepts) at a maximum. From this we infer that f(x) has the most roots.

Answer 2

Thanks ^.^

Answer 3

f(x) has 4
in 0,2pi interval g(x) has 2 intercept
in h(x) power is three so 3 roots