CCSS Support Math II 3.5.15 Example 3

Wendy has $100 that she can pay a contractor to repair her deck. The amount she can pay the contractor per hour can be represented by the rational function , where is the number of hours the contractor takes to finish the repair. Assuming that the domain of the function is all real numbers except the value of where the vertical asymptote of the function’s graph occurs, for what values of is the function undefined? Is this assumption about the domain reasonable in the context of the problem? Why or why not? If not, what are the actual values of for which the function is undefined?
  1. Identify the vertical asymptote of the graph of the function.
  2. Verify the location of the vertical asymptote using a graphing calculator.
  3. Assuming that the domain of the function is all real numbers except the value of where the vertical asymptote occurs, give the value(s) of for which the function is undefined.
  4. Decide whether the assumption about the domain was reasonable.
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