How do you graph #f(x)=3|x+5|#?

1 Answer
Jun 12, 2016

Answer:

See the explanation below

Explanation:

Recall the definition of the absolute value of a real number.

Absolute value of a non-negative number is this number itself, which can be expressed as
IF #R >= 0# THEN #|R|=R#
Absolute value of a negative number is the negation of this number, which can be expressed as
IF #R < 0# THEN #|R|=-R#

Applying this to our function #f(x)=3|x+5|#, we can say that for all #x# that satisfy #x+5 >= 0# (that is, #x>=-5#) we have #|x+5|=x+5#, and our function is equivalent to #f(x)=3(x+5)#.
Its graph looks like
graph{3(x+5) [-10, 10, -5, 5]}

For all other #x# (that is, #x<-5#) we have #|x+5|=-(x+5)#, and our function is equivalent to #f(x)=-3(x+5)#.
Is graph looks like
graph{-3(x+5) [-10, 10, -5, 5]}

To construct a graph of #f(x)=3|x+5|#, we have to take the right side (for #x>=-5#) from the first graph and the left side (for #x<-5#) from the second graph. The result is

graph{3|x+5| [-10, 10, -5, 5]}