A. The domain is the range of values of x for which the function f(x) is defined. The lowest value for x is -4. There is no upper limit for x, because the function is defined for x>1. Therefore, the domain is x=>-4.
B. The range of the function requires us to calculate its value over the domain. For -4<=x<1, the range is 1<=f(x)<6. At x=1, f(x)=9, a singularity. For x>1, f(x)>2 and is unbounded, i.e., goes off to minus infinity as x increases to infinity.
C. The intercepts are where the lines cross the axes. We need to know what value of x makes f(x) zero, and what value of f(x) makes x zero. When x=0, f(x)=5; f(x)=0 when x=3. So the intercepts are (0,5) and (3,0).
D. f(x) is not continuous because when x is just less than 1 f(x) is just less than 6, but it jumps to 9 when x is exactly 1, for that single point alone. After that, when x>1 f(x) goes to 2 from 9.
E. The graph consists of two lines and a singularity. For -4<=x<1, f(x) goes from 1 to just short of 6 in a straight line. The line joins the points (-4,1) and (1,6), cutting the f(x) vertical axis at (0,5). At exactly x=1 we have the single point (1,9), and after that we have a line starting at point (1,2) and cutting the x-axis at (3,0) and going on indefinitely. The first line has a positive slope (/) and the second line a negative slope (\).
I hope this information is clear enough for you to draw the graph.
