(a) Refer to the image below for the graph. (b) domain: $(1, 4)$ range: $(-4, 2)$
Work Step by Step
(a) Sketch the graph of the function by creating a table of values. Plot each point of the table of values then connect them using a line to complete the graph. Note that the domain is restricted to $1 \lt x \lt 4$. Thus, the endpoints $(1, 2)$ and $(4, -4)$ are not part of the graph hence, holes are used to plot them. (refer to the attached image in the answer part above) (b) Use the graph to find the domain and range. The domain is the set that contains all the x-values covered by the graph/function. The range is the set that contains all the y-values covered by the graph/function. Note that: The domain is restricted to $1 \lt x \lt 4$ Thus, the domain is $(1, 4)$. The graph covers the y-values between but not including $-4$ to $2$. Thus, the range is $(-4, 2)$.