Let f be the function defined as follows: f of x equals the piece-wise 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 [x-1]+2 x< 1 ax^2+bx 1=x< 2 5x-10 x> /=2 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 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? 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.

With defined by

in order for it to be continuous at , we require

(i) If and , then and

The limits don't match, so is not continuous at under these conditions.

(ii) To establish continuity at , we'd need the limit as from the right to be equal to the limit from the left, or

(iii) We have and

For to be continuous at , then, we'd need to have

(iv) Taking both requirements from parts (ii) and (iii), we solve for :

I've attached a plot that confirms this is correct.

13

step-by-step explanation:

divide the cost of the total of sodas you bought by the cost of one soda, for example:

$24.57 divided by $1.89 is 13 which means you bought 13 sodas

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.