Algebra 2!
Create your own piecewise function and graph it on the coordinate plane. Explain whether your piecewise function is continuous or discontinuous.

Question

Algebra 2!
Create your own piecewise function and graph it on the coordinate plane. Explain whether your piecewise function is continuous or discontinuous.

anonymous · Answer

ok create you own
do you know that a "piecewise " function is?

anonymous · Answer

yea

anonymous · Answer

what one did  you make up?

anonymous · Answer

i cant figure out how to come up with one

anonymous · Answer

oops

anonymous · Answer

$$f(x) =  \left\{\begin{array}{rcc}
x + 4 & \text{if}  & x < 2 \
x^2& \text{if}  & x \geq 2 
\end{array}
\right.$$

anonymous · Answer

here is another 
$$f(x) =  \left\{\begin{array}{rcc}
\frac{1}{x+3} & \text{if}  & x < 2 \
x^2+x& \text{if}  & x \geq 2 
\end{array}
\right.$$

anonymous · Answer

make up any you like

anonymous · Answer

for the first one is it continuous because it never ends

anonymous · Answer

lol no

anonymous · Answer

continuous would mean they agree at the point where the function changes definition

anonymous · Answer

for example for the first one, $$f(x) =  \left\{\begin{array}{rcc}
x + 4 & \text{if}  & x < 2 \
x^2& \text{if}  & x \geq 2 
\end{array}
\right.$$replace $x$ by $2$ in both expressions

anonymous · Answer

the top one gives $2+4=6$ and the bottom $2^2=4$ and since $6\neq 4$ it is not continuous at $x=2$

anonymous · Answer

thank you so much