Questions: The entire graph of the function g is shown in the figure below. Write the domain and range of g using interval notation. (a) domain = (b) range =

Solution Steps

The domain of a function is the set of all possible input values (x-values) for which the function is defined. From the graph, the function starts at \( x = -4 \) and ends at \( x = 3 \). Both endpoints are included, as indicated by the solid dot at \( x = -4 \) and the open dot at \( x = 3 \).

Since the function is defined from \( x = -4 \) to \( x = 3 \) and includes \( x = -4 \) but not \( x = 3 \), the domain in interval notation is: \[ [-4, 3) \]

The range of a function is the set of all possible output values (y-values). From the graph, the function starts at \( y = 4 \) and decreases to \( y = -2 \). The function includes \( y = 4 \) but not \( y = -2 \).

Since the function is defined from \( y = -2 \) to \( y = 4 \) and includes \( y = 4 \) but not \( y = -2 \), the range in interval notation is: \[ (-2, 4] \]

Final Answer