How do you compare and contrast the graphs of #y=x-2# and #y=(x^2+5x-14)/(x+7)#?
1 Answer
Jan 29, 2018
Explanation:
#"consider "y=(x^2+5x-14)/(x+7)#
#"factorising the numerator gives"#
#y=((x+7)(x-2))/(x+7)#
#"cancelling the factor "(x+7)" from numerator/denominator"#
#y=(cancel((x+7))(x-2))/cancel((x+7))=x-2#
#"the removal of "(x+7)" from the numerator/denominator"#
#"indicates there is a hole at "x=-7#
#rArry=(x^2+5x-14)/(x+7)" reduces to "y=x-2#
#"the graphs of "y=(x^2+5x-14)/(x+7)" and "y=x-2#
#"are the same graph "#
#"the only difference being that "y=(x^2+5x-14)/(x+7)#
#"has a hole at "x=-7" whereas "y=x-2" does not"#
