Fundamentals

Question

1. (a) graph the intervals (-5,3] and (3,∞) on the real number line.
(b) Express the inequalities x≤3 and -1≤ x<4 in interval notation.
(c) Find the distance between -7 and 9 on the real number line.

Answer 1

a) (-5,3], put a circle around the point whose coordinate is -5 but leave the circle unshaded; now put a circle around the point whose coordinate is 3 but this time shade in the circle; finally shade in that part of the number line between the two circles

 

 (3,∞), put a circle around the point whose coordinate is 3 but leave the circle unshaded; now shade in the entire number line to the right of the circle and don't forget to shade in the arrowhead to indicate that the graph goes on indefinitely

 

b) x<3, (-∞,3]

 

-1<x<4, [-1,4)

 

c) l-7-9l=l-16l=16, or l9-(-7)l=l9+7l=l16l=16

 

Answer 2

(a) -----------------------------]

     -5                                     3

 

                                               ----------------------    --------                   -----

                                              3                                             10000000      inf

 

(b)--------------------------------]

   -inf                                     3

 

        [-----------------------------------]

       -1                                            4

 

(c) distance = 9 - (-7) = 9 + 7 = 16 in absolute value that is 16 units