F(x)=(x-1)(x-2)^ list intervals by the x-intercep

Question

Select at least one x- values in each interval and show how it indicates the graph is positive  or negative within that interval

 

and use the result you found to sketch the graph of the  function. Use dashed lines to show the intervals

Answer 1

First, we find the x-intercepts.  The x-intercepts are points that is on the x-axis or the F(x) value is zero.

 

The x-intercepts are x=1 and x=2.  These x-intercepts are your guide.

 

We look at the endpoints of the graph using the lowest x-intercept. 

 

 

If degree of F(x) is even:

F(x) is positive in the interval (-∞, lowest x-intercept).

 

 

If degree of F(x) is odd:

F(x) is negative in the interval (-∞, lowest x-intercept).

 

 

As for the second part, you need to use the degree of the function. The degree of the function tells you how many x-intercepts you will have. You also need to know the multiplicity (number of times the x-intercept appears).  These two things will help you to draw your graph.

 

If the multiplicity is even, then the graph is tangential to the x-axis.

If the multiplicity is odd, then the graph crosses the x-axis.

 

 

Your function is incomplete, so I cannot give more detail than that.