AP Calculus AB Questions and FRQ

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Please be descriptive and detailed in your justification and calculations. Thank you.

Let f be the function defined as follows:

f of x equals the piecewise function absolute value of the quantity x minus one end quantity plus two 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.