Question 987543
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1. &nbsp;f(x) = {{{5-x^2}}}.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of all real numbers &nbsp;(the entire number line).&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;&nbsp;&nbsp;The range is the set of all real numbers &nbsp;x <= 5.

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{{{graph( 240, 160, -5.5, 5.5, -4.5, 6.5,
          5 - x^2
)}}}


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1</B> 

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2. &nbsp;f(x) = {{{sqrt(4-x^2)}}}.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of real numbers &nbsp;-2 <= x <=2. &nbsp;It is the segment &nbsp;[-2, 2].&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The range is the set of real numbers &nbsp;0 <= x <= 2.

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{{{graph( 240, 160, -5.5, 5.5, -4.5, 6.5,
          sqrt(4-x^2)
)}}}


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 2</B> 

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3. &nbsp;f(x) = {{{(x^2-4)/(x-2)}}}.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The domain is the set of real numbers except of &nbsp;x = 2, &nbsp;where the denominator is equal to zero. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The range is the set of all real numbers &nbsp;(the entire number line).


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Notice that &nbsp;f(x) = {{{x + 2}}} &nbsp;everywhere except of &nbsp;x = 2, where it is formally not defined. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If you define &nbsp;f(x) = 0 &nbsp;at &nbsp;x = 2, &nbsp;then you will get a continuous function &nbsp;y = x+2 &nbsp;which coincides with &nbsp;{{{(x^2-4)/(x-2)}}} everywhere where the last function is defined.