Kabbed:
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
Kabbed:
@dude what is a piecewise function I need help
Kabbed:
@Shadow
dude:
Uh create 2 equations (one can be linear and the other could be parabolic)
Kabbed:
it says to write in complete sentences the steps what is the first step?
Kabbed:
this it the last question so I don't know if this question has to do with the other two
dude:
I am just trying to guide you, my goal is to get equations so you understand what to do and then we can format it to answer the question
Kabbed:
so how do I make a linear equation
Kabbed:
@dude
Kabbed:
@Aureo
Kabbed:
@umm @Pixel
Eiwoh2:
@AngeI
Kabbed:
@Elsa213 @Ultrilliam @pooja195 @KittyGirl
Kabbed:
@ZoeyBiocth16
Kabbed:
please even if you might not know even a little help is good
pooja195:
@AngeI @Vocaloid
BlankSpace:
I'm literally feeling for you so let's learn this together
BlankSpace:
You can practice and watch videos on Kahn academy. That's what I do
Kabbed:
sorry I was gone
Kabbed:
what's the first step to create a linear equation
Kabbed:
so a piecewise function is two functions together?
Kabbed:
@dude
Kabbed:
I don't know how to create a linear function
dude:
Oh hold on I've done this with someone before, let me refer you to that post
Kabbed:
Ok
dude:
https://questioncove.com/study#/updates/5c5883d760a4eae76bf54800 I would suggest to not use the same points, change it up a bit or else you might get caught plagiarizing
Kabbed:
y=6x-1 and y=x^4 @dude is that good? or should it be more different
dude:
Thats good
Kabbed:
I don't know what negative to -1 means
dude:
Hmm your first equation is \(6x-1\) or \(6x^{-1}\)?
Kabbed:
6x-1
dude:
Is it the first one or second one I wrote? That doesnt help xD
Kabbed:
the first one @dude
Kabbed:
https://prezi.com/njplm9bmowca/605-algebra-2-assignment/ this is how another student did the piecewise question
Kabbed:
@Shadow
Kabbed:
hero help
Hero:
Are they expecting you to sketch the functions on paper or graphing it on a calculator?
Hero:
By the way, lines of the form y = mx + b are functions that are easy to graph piecewise.
Kabbed:
I can use desmos
Hero:
Piecewise functions are just two different functions that are GRAPHED on their own separate intervals along the x-axis.
Hero:
For example, I can graph \(f(x) = x + 2\) on the interval where \(x < 0\). I can then choose to graph \(g(x) = x^2\) on the interval \(x \ge 0\)
Hero:
Both those functions are easily graphed on desmos btw.
Kabbed:
I see @Hero sorry I'm back
Hero:
Have you attempted to graph the functions in desmos? If so, post a link to your work here.
Hero:
That link goes to a blank page.
Hero:
Here's the one of the easiest functions to graph: https://www.desmos.com/calculator/zchxzybgeh
Kabbed:
f(x)= x+1 x<2 and f(x) = x^4 x>0
Kabbed:
those are my two functions
Hero:
Except your piecewise function has to account for the entire real number domain from \((-\infty, \infty)\). You can split the piecewise function into as many intervals as you want, but it has to account for the entire domain.
Kabbed:
what
Hero:
Also there should not be any interval overlaps between each function piece.
Kabbed:
oh
Hero:
For what you are trying to graph, there is overlap between interval (0, 2).
Hero:
The format to graph a piecewise function in desmos is \(f(x) = \{\text{interval:function, interval:function}\}\)
Kabbed:
I can't do it
Hero:
For example, to graph \(y = x\) on interval \((0, \infty)\) and \(y = 1\) on interval \(-\infty, 0]\), you would write $$f(x) = \{x > 0: x, x \le 0: 1\}$$ https://www.desmos.com/calculator/7oe8mkwxi2
Kabbed:
what
Kabbed:
how do I do f(x)= x+1 x>2 f(x)= x + 2 x<0
Hero:
Is that the current problem you are working on?
Kabbed:
yes
Kabbed:
those are my two functions
Hero:
Well, I can't do it for you unfortunately.
Kabbed:
do what?
Kabbed:
\(f(x) = \{\text{x>2:x+1, x<0:x+2}\}\)
Hero:
Would you mind showing me the original problem your teacher gave you? Can you screenshot it on your computer or take a picture of it with your phone and upload it here?
Hero:
Piecewise functions do not have any overlap
Kabbed:
f(x)= x+1 x>2 f(x)= x + 2 x<0 doesn't overlap
Hero:
Okay, there should not be any gaps either.
Hero:
Now there is a gap on \(0 < x < 2\)
Kabbed:
they both have to be on the same lines
Hero:
no laps or overlaps though.
Kabbed:
f(x)= x+1 x>0 f(x)= x + 2 x<0
Hero:
I can graph three functions: \(f(x) =\begin{cases} x^2, &x<0\\x+2, &0\le x <5\\\sin(x), &x \ge 5\end{cases}\)
Hero:
There is no gaps or overlaps. BTW, an open circle point is considered a gap.
Hero:
Yes but now a gap occurs at \(x = 0\)
Hero:
You've accounted for the interval between infinity and zero and between zero and infinity, but what happens when x = 0?
Kabbed:
I don't know
Hero:
you need to include the equal sign on one of those intervals
Hero:
Great effort so far though @Kabbed
Hero:
You're learning by trial and error. The best way to learn.
Kabbed:
f(x)= x+1 x<2 f(x)= x-4 x<3
Hero:
Have you tried graphing that in desmos?
Hero:
Your previous attempt was better. It was only missing an equal sign on one of the intervals. This current attempt is worse though because there is too much overlap on interval \(-\infty < x < 2\) and a big gap on interval \(3 < x < \infty\)
Kabbed:
how do I put a equal sign on one of them?
Hero:
add an equal sign next to the inequality sign.
Kabbed:
f(x)= x+1 x>=0 f(x)= x + 2 x<0
Hero:
Much better
Hero:
Now you just have to graph that in desmos.
Hero:
Yeah, that works, but it is the simplest kind of graph.
Kabbed:
x>0 is a constraint or a interval what do I call it
Hero:
In that form you can call it a constraint.
Hero:
Basically a constraint is a limitation you place on \(x\). You constrain it by saying the function is only valid when \(x > 0\). In other words, the function is only valid when \(x\) is greater than zero.
Hero:
If you write \((0, \infty)\) then you mean that the function exists on the interval between zero and infinity.
Hero:
But essentially \(x > 0\) and \((0,\infty)\) operate the same way. They both place limitations on the domain of the function.
Hero:
So if someone asks "What is the constraint on the function?". You can respond with something like "The constraint on the function is \(x > 0\).". However, if they ask "On what interval does the function exist?", you can say something like "The function exists on interval \((0, \infty)\)
Kabbed:
The next step, is to plot the rest of the points but only the ones to the left of 1 on the x-axis. Lastly connect the lines. Repeat the same steps for the second function but according to its numbers. @Hero
Kabbed:
ill try to write that^
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