We are given the graph of a function, which we are told that is polynomial of degree 4.
Recall that the domain of a function is the values of x for which the the function is defined. Using the graph, the domain is the set of x coordinates of the point s of the graph.
On the other side, recall that the range of a function is the set of values that the function takes. So, using the graph, the range is the set of y coordinates of the points of the graph.
Since we know that the graph is from a polynomial of degree 4, we recall that polynomials of any degree are defined for every value of x. Then, the domain of this graph is (-infinity, infinity).
On the other side, to determine the range. we take a look at the y coordinates of the graph. So the highest value from the graph is 7. Also, we see that the polynomial decreseases its value as x gets bigger or smaller. This behavior stays true globally, so, we can say that the range of the function is the interval (-infinity,7].