Determine c and d so that f(x) is continuous?

all this is is a system of equations problem.

for it to be cont. all three must have a value of 2 at x = 3 (just plug this in each equation) you do not have to worry about the second equation but look at the top and bottom equations.

plug in 3 as x in each equation and you will get 27+3c+d=2

9+c+9d=2

multiply the bott eq by 3 and then solve for d. then plug the value for d into either the top or bottom eqs.

you will find c. fx is cont when c is -109/13 and when d is 2/13

to be sure that f(x) to be non-end at x = -2, then the linked fee of f(x) for the three diverse definitions would desire to be the comparable at x = -2 5x^2 + cx + 9 at x = -2 ==> 5(-2)^2 + c(-2) + 9 = 5(4) + 9 - 2c = 0 29 - 2c = 0 ==> c = 29/2 dx^2 + 9x + 29/2 = 0 at x = -2 d(-2)^2 + 9(-2) + 29/2 = 0 4d - 18 + 29/2 = 0 4d = 36/2 - 29/2 = 7/2 d = 7/8 so if c = 29/2 and d = 7/8, then f(x) is non-end at x = -2 (and all connect on the factor (-2 , 0)