Compare the functions shown below:

f(x) = x3 + 2x2 − 4x − 3
g(x)

polynomial graph with x intercepts at negative 2, negative 1, 1, 3, y intercept at 6
h(x)

trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
over the interval x = 0 to x = 2π

which function has the most x-intercepts?

The function f(x) = x^3 + 2x^2 - 4x - 3 is a polynomial function of degree 3 and hence will have three solutions and hence 3 x-intercepts. The function g(x) has x-intercepts at x = -2, x = -1, x = 1 and x = 3. Hence function g(x) has 4 x-intercepts. The function h(x) has x-intercepts at points (pi over 2, 0) and (3 pi over 2, 0). Hence function h(x) has 2 x-intercepts. Therefore, the function with the most x-intercepts is function g(x) with 4 x-intercepts.