Answer:
To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.
X-intercepts:
The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:
3x³-12x²-15x = 0
This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.
Y-intercepts:
The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:
f(0) = 3(0)³ - 12(0)² - 15(0) = 0
So the y-intercept of the graph is at the point (0,0)
In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)
Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.
Explanation: