Question

Select the correct answer. What is the range of the function f(x) = -4\x+ 11 - 5? A. (-4,-5) B. [-5,-) OC. (-4,-) OD. (-2,-4] Reset Next 2021 Edmentum. All rights reserved. Search

Answer 1

We are given the following function:

$f(x)=-4\lvert x+1\rvert-5$

This function is equivalent to the function:

$g(x)=-4\lvert x+1\rvert$

Together with a translation 5 units in the negative direction of the "x" axis. Since the range of g(x) is all the values of "y" that are smaller or equal to zero, if we translate 5 units in the negative direction of the y-axis the range is:

$R(f(x))=\mleft\lbrace y\parallel y\mright?\le5\rbrace$

or in interval notation:

$R(f(x))=(-\infty,-5\rbrack$