# Thread: make me continuous

1. ## make me continuous

Find the values of a and b that make f continuous everywhere.

I see a polynomial. should I factor it? I kinda want to factor it haha.

anyway, I know I gotta focus on x=3. If I can get the two points to be continuous there, I should be good, right?

2. Hello,
Originally Posted by leftyguitarjoe

Find the values of a and b that make f continuous everywhere.

I see a polynomial. should I factor it? I kinda want to factor it haha.

anyway, I know I gotta focus on x=3. If I can get the two points to be continuous there, I should be good, right?
There's no need to factor the polynomial (the second one ).

You gotta focus on x=3 but also on x=1 !
And yes, it should be good.

Let $f_1(x)=\frac{x^2-1}{x-1}=x+1$, $x<1$
Let $f_2(x)=ax^2-bx+5$, $1 \le x<3$
Let $f_3(x)=2x-a+b$, $x \ge 3$

A function is continuous at x=a if :
$\lim_{\substack{x \to a \\ xa}} f(x)$
So for example at x=1 :
$\lim_{\substack{x \to 1 \\ x<1}} f(x)=\lim_{x \to 1} f_1(x)$

and $\lim_{\substack{x \to 1 \\ x>1}} f(x)=\lim_{x \to 1} f_2(x)$

Same for x=3, see what expression it is if x<3 and if x>3

3. oh, I see now. The limits should be the same when approaching from the left and right?

4. Originally Posted by leftyguitarjoe
oh, I see now. The limits should be the same when approaching from the left and right?
Yes

5. Originally Posted by Moo
Yes
cool! thanks!