# find values for m and n so function is continuous

• Jun 6th 2012, 07:59 PM
sluggerbroth
find values for m and n so function is continuous
f(x)= mx, x<3
n, x=3
-2x+9 x>3
• Jun 6th 2012, 09:17 PM
pickslides
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.
• Jun 7th 2012, 04:16 AM
Plato
Re: find values for m and n so function is continuous
Quote:

Originally Posted by sluggerbroth
f(x)= mx, x<3
n, x=3
-2x+9 x>3

You want to find $\displaystyle m~\&~n$ so that $\displaystyle {\lim _{x \to {3^ + }}}f(x) = {\lim _{x \to {3^ - }}}f(x)$.
• Jun 7th 2012, 08:17 AM
Soroban
Re: find values for m and n so function is continuous
Hello, sluggerbroth!

Quote:

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

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

Make a sketch.

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

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

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

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

Code:

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Can you work it out?