Question

g(x) = (x + 7)(x + 1)(x − 1)


3. Create a graph of the polynomial function you selected from Question 2.

Answer 1

Answer:

Graph attached below

Step-by-step explanation:

Graph of a Function

Assuming we are given an explicit expression for a real function g that depends on only one variable x. The graphic representation of g can be obtained by giving the independent variable x a set of values for each of which we can compute the corresponding values of g. We'll get a series of ordered pairs of the form (x,g(x)).

Then, we can locate each point in a rectangular grid and join all the points with strokes until a smooth graph is shown. We can safely join them because the domain of g consists of real numbers, not just the specific points we selected.

The function to graph is

$g(x) = (x + 7)(x + 1)(x -1)$

We can see the roots of the polynomial are x=-7, x=-1, x=1, thus the range of values for x should cover all of them. We have selected

x={-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3}

And computed the values of g as indicated in the table below. The resulting graph is also shown in the second image attached