the function f(x)=(3x² - 11x - 4)/(x + 2) is a rational function. answer parts (a) - (i).\nh. plot points…

the function f(x)=(3x² - 11x - 4)/(x + 2) is a rational function. answer parts (a) - (i).\nh. plot points, choosing values of x between each intercept and values of x on either side of all vertical asymptotes. substitute values of x into f(x) and simplify.\n(-11/4,f(-11/4))=(-11/4,-261/4)\n(-1,f(-1))=(-1,10)\n(3,f(3))=(3,-2)\n(5,f(5))=(5,16/7)\n(type ordered - pairs, using integers or fractions.)\ni. sketch the graph. choose the correct graph.

the function f(x)=(3x² - 11x - 4)/(x + 2) is a rational function. answer parts (a) - (i).\nh. plot points, choosing values of x between each intercept and values of x on either side of all vertical asymptotes. substitute values of x into f(x) and simplify.\n(-11/4,f(-11/4))=(-11/4,-261/4)\n(-1,f(-1))=(-1,10)\n(3,f(3))=(3,-2)\n(5,f(5))=(5,16/7)\n(type ordered - pairs, using integers or fractions.)\ni. sketch the graph. choose the correct graph.

Answer

Explanation:

Step1: Analyze the given points

We are given the ordered - pairs ((-\frac{11}{4},-\frac{261}{4})), ((-1,10)), ((3, - 2)), ((5,\frac{16}{7})). We need to plot these points on the coordinate plane and then determine which graph among the options matches the general shape and position of the points.

Step2: Evaluate the behavior of the rational function

The rational function (f(x)=\frac{3x^{2}-11x - 4}{x + 2}). First, we can factor the numerator: (3x^{2}-11x - 4=(3x + 1)(x - 4)). So (f(x)=\frac{(3x + 1)(x - 4)}{x + 2}), and it has a vertical asymptote at (x=-2). We can also find the (x) - intercepts by setting (y = 0), so ((3x + 1)(x - 4)=0), which gives (x=-\frac{1}{3}) and (x = 4), and the (y) - intercept by setting (x = 0), (y=\frac{-4}{2}=-2).

Step3: Match with the graphs

By plotting the given points and considering the asymptotes and intercepts, we can determine the correct graph.

Answer:

(No answer is provided as the actual graphs A - F are not described in detail. To fully answer, one would need to analyze the position of the points and asymptotes on each of the given graphs.)