Do not use your calculator for parts 1 through 4.

let f be the function defined as follows:

{ 3-x, for x < 1
f(x) = { ax^2 + bx, for 1 ≤ x < 2
{ 5x-10, for x ≥ 2

where a and b are constants

the equation in written form: 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.