To answer this question, we need to know that when it is mentioned that we need to determine the right-hand and left-hand behavior of the graph, we have to determine what happens with the function when the values for the independent variable, x, increase (right-hand) and when the same independent variable decreases (left-hand).
We can use a graphing calculator to graph that function as follows:
This is the graph for the function:
[tex]f(x)=\frac{x^4+3}{4}[/tex]
As we can see, when the values of x tend to infinity (positive infinity), right-hand behavior, the values of y tend to positive infinity (rises to the right).
We can also see that when the values of x tend to negative infinity (-∞), the values of y tend to positive infinity too (rises to the left).
Therefore, in summary, we can say that the behavior of the graph is:
• Rises to the left, Rises to the right (second option)
