B. 38.98 cant be a c or D
The answer choice which explains whether the function is a direct variation or not is; This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
<h3>Which explains whether or not the function represents a direct variation?</h3>
It follows from the task content that the function passes through the origin and hence, if the function was represents as a linear function, it's y-intercept would be zero.
Furthermore, the slope, otherwise termed it's rate of chage is constant and is evaluated as; $5 per hour. Hence, the aforementioned form the basis for the classification of the function as a direct variation.
Read more on variation;
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<u>Step-by-step </u><u>explanation</u>:-
<u>To </u><u>verify</u>:-
Hence verified.
We have that
<span>(c-4)/(c-2)=(c-2)/(c+2) - 1/(2-c)
</span>- 1/(2-c)=-1/-(c-2)=1/(c-2)
(c-4)/(c-2)=(c-2)/(c+2)+ 1/(c-2)------- > (c-4)/(c-2)-1/(c-2)=(c-2)/(c+2)
(c-4-1)/(c-2)=(c-2)/(c+2)---------------- > (c-5)/(c-2)=(c-2)/(c+2)
(c-5)/(c-2)=(c-2)/(c+2)------------- > remember (before simplifying) for the solution that c can not be 2 or -2
(c-5)*(c+2)=(c-2)*(c-2)------------------ > c²+2c-5c-10=c²-4c+4
-3c-10=-4c+4----------------------------- > -3c+4c=4+10----------- > c=14
the solution is c=14
the domain of the function is (-∞,-2) U (-2,2) U (2,∞) or
<span>all real numbers except c=-2 and c=2</span>
