The graph of the function g(x) = 0.5x3 + 4 is a cubic function. This type of graph typically has an S-like shape, and the coefficient of the x3 term determines its steepness and direction.
In this case, since the leading coefficient (0.5) is positive, the ends of the graph will rise in both directions. The ‘+ 4’ in the equation means that the entire graph is shifted upwards by 4 units on the y-axis.
To visualize this, you can plot several key points. For example:
- g(0) = 0.5(0)3 + 4 = 4
- g(1) = 0.5(1)3 + 4 = 4.5
- g(-1) = 0.5(-1)3 + 4 = 3.5
- g(2) = 0.5(2)3 + 4 = 8
- g(-2) = 0.5(-2)3 + 4 = -2
These points give you a basic outline of the graph. As you continue plotting points, you’ll see the S-shape become more defined. To draw the graph, connect the points smoothly, which reflects the continuous nature of cubic functions.