Questions: The graph of y=K(x) is given. (a) Write the domain of K. (b) Write the range of K.

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, we observe that the function \( K(x) \) is defined from \( x = -5 \) to \( x = 5 \). However, at \( x = -5 \), there is an open circle, indicating that the function is not defined at this point. Therefore, the domain of \( K \) is: \[ (-5, 5] \]

The range of a function is the set of all possible output values (y-values) that the function can take. From the graph, we observe that the lowest y-value is \( -2 \) and the highest y-value is \( 5 \). The function includes these values, as indicated by the filled circles at these points. Therefore, the range of \( K \) is: \[ [-2, 5] \]

Final Answer