Question

describe and correct the error a student made in determining the relationship between the domain and range of ( f(x) = 10|x| ) and ( f(x) = |x| ).

the domain of ( f(x) = 10|x| ) is the same as the domain of ( f(x) = |x| ).
the range of ( f(x) = 10|x| ) is 10 times the range of ( f(x) = |x| ) (\boldsymbol{\times})

choose the correct answer below.

a. the domain is not the same for both functions. the domain of the function ( f(x) = |x| ) is 10 times the domain of ( f(x) = 10|x| ). the range of ( f(x) = 10|x| ) is not 10 times the range of ( f(x) = |x| ). the range is the same for both functions, ( y geq 0 ).

b. the domain is not the same for both functions. the domain of the function ( f(x) = |x| ) is 10 times the domain of ( f(x) = 10|x| ).

c. the range of ( f(x) = 10|x| ) is not 10 times the range of ( f(x) = |x| ). the range is the same for both functions, ( y geq 0 ).

d. the domain is not the same for both functions. the domain of the function ( f(x) = 10|x| ) is 10 times the domain of ( f(x) = |x| ). the range of ( f(x) = 10|x| ) is not 10 times the range of ( f(x) = |x| ). the range of ( f(x) = |x| ) is 10 times the range of ( f(x) = 10|x| ).

Explanation:

Answer:

C. The range of $f(x)=10|x|$ is not 10 times the range of $f(x)=|x|$. The range is the same for both functions, $y \geq 0$.