Question

for what value of the constant c is the function
f(x) =\[\left[\begin{matrix}x+c & if x <2 \\ cx^2+1 & if x \ge 2\end{matrix}\right]\]
continuous at every number?

Answer 1

ok lets walk through this together

Answer 2

if you plug in 2 for each of d equations in d piece wise what do u get

Answer 3

2+c
4c+1 ?

Answer 4

ok equate them to each other and simplify

Answer 5

what do u get?

Answer 6

oh okay...

Answer 7

is it 1/3?

Answer 8

correct

Answer 9

yay! but why do you mean to sub in the 2 for?

Answer 10

Ok because if u notice d graph splits at two.....therefore the two is our point of interest

Answer 11

and all u need to do is plug it into x

Answer 12

oh i see, so the restrictions do give info... thanks!

Answer 13

yep