# Math Help - find values for m and n so function is continuous

1. ## find values for m and n so function is continuous

f(x)= mx, x<3
n, x=3
-2x+9 x>3

2. ## Re: find values for m and n so function is continuous

First pick a value for x>3 i.e. x=4 then solve n such that -2(4)+9 = n

Once you know what n is then for x=3, solve mx=n, will give you m.

3. ## Re: find values for m and n so function is continuous

Originally Posted by sluggerbroth
f(x)= mx, x<3
n, x=3
-2x+9 x>3
You want to find $m~\&~n$ so that ${\lim _{x \to {3^ + }}}f(x) = {\lim _{x \to {3^ - }}}f(x)$.

4. ## Re: find values for m and n so function is continuous

Hello, sluggerbroth!

$\text{Find values for }m\text{ and }n\text{ so that }f(x)\text{ is continuous.}$

. . $f(x) \;=\;\begin{Bmatrix}mx & \text{ if } x < 3 \\ n & \text{ if }x = 3 \\ -2x+9 & \text{ if }x > 3 \end{array}$

Make a sketch.

When $x < 3$, we have a line through the origin with slope $m.$

When $x = 3$, we have a point $(3,n).$

When $x > 3$, we have the line $y \:=\:-2x + 9$
. . It has y-intercept 9 and slope -2.

We want the three graphs to "meet" at $x = 3.$

Code:
     \|
*
|\
| \
|  \
|   \
|    \
|     \     *
|      \  *
|       o
|     * :\
|   *   : \
| *     :  \
- - * - - - + - * - -
* |       3    \
|
Can you work it out?