5 short answer calc questions

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5 short answer calc questions

Do not use your calculator for Parts 1 through 4.

Let f be the function defined as follows:

f of x equals the piecewise function three minus x for x is less than one, a x squared plus b x for one is less than or equal to x is less than two, and five x minus ten for x is greater than or equal to two where a and b are constants.

  1. If a = 2 and b = 3, is f continuous at x = 1? Justify your answer.
  2. Find a relationship between a and b for which f is continuous at x = 1.
    Hint: A relationship between a and b just means an equation in a and b.
  3. Find a relationship between a and b so that f is continuous at x = 2.
  4. Use your equations from parts (ii) and (iii) to find the values of a and b so that f is continuous at both x = 1 and also at x = 2?
  5. Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into the document.

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