y=(x-2)(x-3)(x+5)

Question

y=(x-2)(x-3)(x+5)

 

1- Determine the end behavior of the function.                                                                       
2- Find all x-intercepts.                                                                                                             

  3- Find all y-intercepts.                                                                                                                

4- Use the x-intercepts to divide the x axis into intervals.                                                        
5- Choose at least one point within each interval to show whether the function is positive or negative.                     

 

 

Im mainly concerned about questions  4 & 5.. i just dont know if you need the rest of these questions to answer those. Thank you

                                                                                                                   

Answer 1

You need the result from 2 to do 4 & 5

 

The x-intercepts are the values of x for which y = 0.  In this case they are x = 2, 3 and -5.  

 

These x-intercepts divide the x-axis into 4 intervals 

 

(-∞,-5), (-5,2), (2,3), and (3,∞) 

 

If you pick a point from the 1st interval like -6, you will see that all 3 of the factors are negative so the function is negative.  

 

If you pick a point from the 2nd interval like 0, you will see that 2 of the factors are negative and one is positive so the function is positive.  

 

If you pick a point from the 3rd interval like 2.5, you will see that 1 of the factors is negative and 2 are positive so the function is negative.  

 

If you pick a point from the 4th interval like 4, you will see that all 3 of the factors are positive so the function is positive.  

 

You should actually evaluate the function at each of these points to show what the value is.