Final answer:
The correct answer is option A. The intercepts of a third-order polynomial are the points where it crosses the x-axis and y-axis, which corresponds to option A) x, y.
Step-by-step explanation:
The intercepts of a third-order polynomial are the points where the polynomial crosses the x-axis and y-axis. These points of intersection are found where the polynomial's value is zero. To find the x-intercepts (also known as roots or zeros), you solve for x in the polynomial equation when y is set to zero. To find the y-intercept, you solve for y when x is set to zero, which is typically easier as it's simply the constant term in the polynomial's standard form, assuming the polynomial is written as f(x) = ax^3 + bx^2 + cx + d.
Intercepts are essential in graphing and understanding the behavior of polynomials. Graphically, x-intercepts are the points where the graph crosses the horizontal axis, and the y-intercept is the single point where the graph crosses the vertical axis.
The correct answer to the student's question is: The intercepts of a third-order polynomial are the points where the polynomial crosses the x and y axes. Hence, the correct option is A) x, y.