Question

f(x)={ kx+1, x<1 and x^2, x is greater or equal to 1} a)find the value of k so that f(x) is continuous at x=1
b) using the value of k found part a) sketch the graph of f(x)

Answer 1

in order for the function to be continuous, lim f(x) = 1 x->1^-

Answer 2

do you understand?

Answer 3

no:(

Answer 4

this is much easier than it looks
put \(x=1\) in both expressions, set them equal, solve for \(k\)

Answer 5

so put k(1)+1=(1)^2 ?

Answer 6

yep

Answer 7

I got k=0?

Answer 8

me too

Answer 9

me 3

Answer 10

how would I graph this?

Answer 11

Just make a piecewise graph....

f(x)={ 1, x<1
={x^2 x>=1

Both pretty basic functions. :)

Answer 12

thank you:) i think i got it now