Answer:
To graph the given cubic function f(x) = 0.3x^3 - x^2 + 5x + 100 and label the x and y intercepts, we need to follow these steps:
1. Find the x-intercepts: Set f(x) = 0 and solve for x.
0.3x^3 - x^2 + 5x + 100 = 0
This is a cubic equation, so we can use factoring, the quadratic formula, or numerical methods to find the roots (x-intercepts).
2. Find the y-intercept: Substitute x = 0 into the equation to find the corresponding y-value.
f(0) = 0.3(0)^3 - (0)^2 + 5(0) + 100 = 100
The y-intercept is (0, 100).
3. Plot some points on the graph by substituting x-values into the equation and finding the corresponding y-values.
4. Connect the points smoothly to form the cubic curve.
5. Label the x-intercepts by marking the points where the graph crosses the x-axis.
6. Label the y-intercept by marking the point (0, 100) on the y-axis.
