The function that has the most x-intercept is given by: Option A: f(x)
What is x-intercept of a function?
The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.
The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 becuase at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
What is the maximum number of roots a polynomial equation can have?
Suppose that we've got a polynomial function as y = p(x),
where p(x) is of degree n (the highest power its variable pertains in any of its composing terms).
Then, the maximum number of roots it can possess for p(x) = c (c is a constant), or p(x) - c = 0 is n
So, the number of roots of p(x) - c = 0 cannot exceed the degree of p(x).
From the graph, we see that:
f(x) intersects x-axis at 4 places, so it has 4 x-intercepts.
g(x) intersects the x-axis at 2 places as in the graph, and therefore, it has 2 x-intercepts.
h(x) is a polynomial of degree 3. The maximum number of intercepts it can have is the maximum number of roots h(x) = 0 can have which is 3(the degree of h(x) ). So it cannot be bigger than 3.
Thus, the function that has the most x-intercept is given by: Option A: f(x)
Learn more about x-intercept here:
https://brainly.com/question/14764115
