The graphs of ๐ฆ = 2๐ฅ and ๐ฆ = ๐ฅ2 are shown here:
Identify two major differences in behavior
One major difference in behavior is that the function ๐ฆ = ๐ฅ2 has a minimum value at the vertex (0,0), while the function ๐ฆ = 2๐ฅ does not have a minimum or maximum value.
Another major difference in behavior is that the function ๐ฆ = ๐ฅ2 is a nonlinear function, meaning that its rate of change is not constant, while the function ๐ฆ = 2๐ฅ is a linear function, meaning that its rate of change is constant.
Two major differences in behavior between the graphs of y = 2x and y = x^2 are:
1. Direction of the curves: The graph of y = 2x is a straight line with a positive slope, meaning it increases in a linear fashion as x increases. On the other hand, the graph of y = x^2 is a parabola that opens upwards.
2. Rate of change: The slope of the line y = 2x remains constant, meaning it has a constant rate of change. However, the slope of the parabola y = x^2 varies at different points, indicating that the rate of change is not constant but instead increases as x increases.