Final answer:
Finding x-intercepts of a polynomial function using a calculator determines the roots of the function, which are the values of x where the function value is zero and the graph crosses the x-axis. Option A is the correct answer.
Step-by-step explanation:
When we talk about finding the x-intercepts of a polynomial function, we are referring to the specific points where the graph of the function crosses or touches the x-axis. These points are significant because they represent the roots of the function, which are the values of x for which the value of the function is zero. To find the x-intercepts using a calculator, one would typically input the polynomial and use the calculator's root-finding feature to solve for x.
The x-intercept(s) of a polynomial function provide important information about the function's behavior. If a polynomial is of degree n, it can have up to n real roots, although some roots may be repeated or not be real numbers. The process of finding x-intercepts usually involves setting the function equal to zero and solving for the values of x that satisfy this equation. This might require factoring the polynomial, using the quadratic formula, or applying numerical methods if the polynomial is of a higher degree and cannot be easily factored.
It is worth noting that the question's options might reference other concepts. For instance, the y-intercept is the point where the graph crosses the y-axis, which is found by evaluating the polynomial at x = 0. Critical points are points on the graph where the first derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection. Asymptotes refer to lines that the graph of a function approaches but never actually reaches, which are particularly relevant for rational functions rather than polynomial functions.
Therefore, the correct answer to the question "Finding x-intercepts of a polynomial function calculator determines:" is: A) Roots of the function