How do you graph, find the zeros, intercepts, domain and range of #f(x)=abs(4x)#?

1 Answer
Alan N.
Feb 20, 2017

Graph: A straight line from the origin of slope 4, with a miror reflection about the #y # axis.
#f(0)=0#, Domain: #(-oo, +oo)#, Range: #(0, +oo)#

Explanation:

#f(x) =abs(4x)#

#f(x) =4x# for #x>0# [A straight line from the origin of slope 4]
and
#f(x) =-4x# for #x<0# [A straight line from the origin of slope -4]
and
#f(x) =0# for #x=0# [The single zero and intercept of #f(x)#]

#f(x)# is defined #forall x -># The domain of #f(x)# is #(-oo, +oo)#

#f(x) >=0 forall x -># The range of #f(x)# is #(0, +oo)#

These can be seen from the graph of #f(x)# below:

graph{abs(4x) [-11.21, 11.29, -2.145, 9.105]}

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