Consider the basic upward parabola y=x^2
In this parabola as the x increases toward positive infinity , does the y value also increase toward infinity?
If so does it increase faster or slower than the x?
yes, faster, it increases as the square of x.
To determine whether the y-value increases toward infinity as x increases toward positive infinity in the parabola y = x^2, you can analyze the behavior of the function.
When x increases, the value of x^2 also increases. This means that the y-values will increase as well. In fact, the y-values increase faster than the x-values because the relationship between x and y in this parabola is quadratic.
A quadratic relationship means that the y-values increase as the square of the x-values. For example, when x = 1, y = 1^2 = 1. When x = 2, y = 2^2 = 4. When x = 3, y = 3^2 = 9. As you can see, the y-values increase much faster than the x-values.
As x approaches positive infinity, the y-values will also approach positive infinity but at a faster rate due to the quadratic relationship between x and y.