Question 984605

1) &nbsp;f(x) = 1-|x|. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers. &nbsp;&nbsp;The range is the set of all real numbers <= 1. 


2) &nbsp;f(x) = {{{x^2-1/x-1}}}. &nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers =/= 0. &nbsp;&nbsp;The range is the set of all real numbers.

<TABLE> 
  <TR>
  <TD> 

{{{graph( 200, 200, -4.5, 4.5, -4.5, 4.5,
          x^2 - 1/x -1
)}}}


<B>Figure</B>. Plot of the function {{{x^2 - 1/x - 1}}}
  </TD>
  </TR>
</TABLE>


3) &nbsp;f(x) = -|x|. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers. &nbsp;&nbsp;The range is the set of all non-positive real numbers.


4) &nbsp;f(x) = |x-1|. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers. &nbsp;&nbsp;The range is the set of all non-negative real numbers.


5) &nbsp;f(x) = {{{(abs(x-2))/(2-x)}}}. &nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers =/= 2. &nbsp;&nbsp;The range is &nbsp;{-1, 1}, &nbsp;i.e. &nbsp;the set consisting of two numbers &nbsp;-1&nbsp; and &nbsp;1&nbsp; only. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Actually, &nbsp;this function is equal to &nbsp;1&nbsp; at x < 2 &nbsp;and equal to &nbsp;-1&nbsp; at x > 2). 


6) &nbsp;f(x) = {{{sqrt(3-2x)}}}. &nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers x <= {{{3/2}}}. &nbsp;&nbsp;The range is the set of all non-negative real numbers. 


<TABLE> 
  <TR>
  <TD> 

{{{graph( 200, 200, -4.5, 4.5, -4.5, 4.5,
          sqrt(3-2x)
)}}}


<B>Figure</B>. Plot of the function {{{sqrt(3-2x)}}}
  </TD>
  </TR>
</TABLE>