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

1 Answer
Zor Shekhtman
Jun 12, 2016

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

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

For all other xx (that is, x<-5x<−5) we have |x+5|=-(x+5)|x+5|=−(x+5), and our function is equivalent to f(x)=-3(x+5)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|f(x)=3|x+5|, we have to take the right side (for x>=-5x≥−5) from the first graph and the left side (for x<-5x<−5) from the second graph. The result is

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

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