f(x)= mx, x<3
n, x=3
-2x+9 x>3
Hello, sluggerbroth!
$\displaystyle \text{Find values for }m\text{ and }n\text{ so that }f(x)\text{ is continuous.}$
. . $\displaystyle f(x) \;=\;\begin{Bmatrix}mx & \text{ if } x < 3 \\ n & \text{ if }x = 3 \\ -2x+9 & \text{ if }x > 3 \end{array}$
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 $\displaystyle x = 3.$
Can you work it out?Code:\| * |\ | \ | \ | \ | \ | \ * | \ * | o | * :\ | * : \ | * : \ - - * - - - + - * - - * | 3 \ |