Questions: The graphs for different functions are given below. For each function state the domain and range of the function using interval notation, Also, state the values of x where the functions are increasing and where they are decreasing. Finally, state whether or not there are any values of y for which the value of the function is equal to y for more than one value of x.

Solution Steps

The domain is the set of all possible x-values. The x-values extend from -2 to 3 inclusive. Thus, the domain in interval notation is [-2, 3]. The range is the set of all possible y-values. The y-values extend from -2 to 2 inclusive. Thus, the range in interval notation is [-2, 2].

The function is increasing when the y-value increases as the x-value increases. This occurs from x = -2 to x = 1 and from x = 1 to x = 3. Thus, the function increases on the interval [-2, 1) and (1, 3]. The function is neither increasing nor decreasing at the hollow circle at x=1.

The function is not decreasing in any interval.

For the part of the graph where the function is increasing, there is no value of y for which the value of the function is equal to y for more than one value of x.

Final Answer