Question

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.

If a = 2 and b = 3, is f continuous at x = 1? Justify your answer.

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.

Find a relationship between a and b so that f is continuous at x = 2.

Use your equations from