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

1 Answer
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]}