Question

Compare the functions shown below:

f(x)

polynomial graph with x intercepts at negative 3, negative 2, 1, 2, y intercept at negative 12
g(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
h(x) = 2x3 − 2x2 − 3x + 2


Which function has the most x-intercepts? (2 points)

f(x)

g(x)

h(x)

All three functions have the same number of x-intercepts.

Answer 1

f(x) has the most x intercepts

Answer 2

The function f(x) has the most x-intercepts, with five x-intercepts at -3, -2, 1, 2, and the y-intercept at -12. The function g(x) has only three points given, and therefore cannot be determined how many x-intercepts it has. The function h(x) has at most three x-intercepts, which can be found by graphing or using calculus techniques. Therefore, the correct answer is:

f(x)