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[3 points] Sketch the graph of the piecewise function: (6 - x if x < 2 x-6 if x22 The "window" of your hand-sketched graph should be _5 < x < 5 a...

Question

[3 points] Sketch the graph of the piecewise function: (6 - x if x < 2 x-6 if x22 The "window" of your hand-sketched graph should be _5 < x < 5 and ~10 <y < 10[4 points] Sketch the graph of the piecewise function: if x <-2 ~X+1 if _ 2 <x <3 x2/4 if x >3The "window" of your hand-sketched graph should be -5 < x < 5 and10 < y < 10[8 points] The monthly charges of the Central Texas Gas Company are as follows:Gas Used First 75 cubic meters Ne

[3 points] Sketch the graph of the piecewise function: (6 - x if x < 2 x-6 if x22 The "window" of your hand-sketched graph should be _5 < x < 5 and ~10 <y < 10 [4 points] Sketch the graph of the piecewise function: if x <-2 ~X+1 if _ 2 <x <3 x2/4 if x >3 The "window" of your hand-sketched graph should be -5 < x < 5 and 10 < y < 10 [8 points] The monthly charges of the Central Texas Gas Company are as follows: Gas Used First 75 cubic meters Next 100 cubic meters Next 250 cubic meters Above 425 cubic meters Charge 523.00 minimum cost 126 per cubic meter 9c per cubic meter 6c per cubic meter (a) Construct a function that can be used to compute the monthly gas bill (b) Use the function to find the costs of 260 and 830 cubic meters of gas.



Answers

Graph each step function. See Examples 5 and 6 The cost of parking a car at an airport hourly parking lot is $\$ 3$ for the first half-hour anc S2 for each additional half-hour or fraction thereof. Graph the function defined b $=$ $y=f(x)=$ the cost of parking a car for $x$ hours. Use the interval $(0,2]$

I think the best way to go about these problems is to make an input output table like the one I have here on the left. So let's choose a value for X. Um, so let's say X is equal to zero. Then we'll look to the equations and see which condition it matches. So when x zero The first condition is satisfied, so we'll use the first equation. So when X is equal to zero, F of X is equal to zero. So let's put that on the graph here. Then let's say X equals two. This is still part of the first condition, so f of X is equal to three goes right around here. Then let's pick X equals three. Then this now satisfies thes second equation. So F of X is equal to four. And let's pick X equal six, which is also part of the second condition. And so we find ffx is equal to fart. Then let's say X you holes nine and there's no longer satisfies the first or second condition. So we're left with the third and last one, so f of X is equal to four. Okay, and let's a X is equal to 10 again. We'll use the last equation so f of X equals three. Yeah, let's say I know the X is equal to 11 again. Last equation and F of X equals zero. Okay, so now when we connect these points, we want to keep in mind the bounds and look at the behavior. So the first equation between the first parents, we see that it's a line so will simply draw a line in the 1st 2 courts. Then, for the second equation, we'll see that that's no longer line, but isn't home a function of root X So should look something like this, and it has a curve. Now, the last equation is also a function of root X. So it should look something like this also with Baker. This is what paragraph looks like.

Hey, guys, welcome back This problem. Want to start by finding the graph? We noticed that for the 1st 25 therms it is 75 cents per therm venerated graphic on a slope of zero 75 or of 3/4. And if we think about it, it has to include the origin, cause if you have a zero therms p $0 so reliance linear lines to a through the origin. So our equation of our line will be suit. Why is you go to 3/4 x zero is there? Why intercept Must be zero. I mean, as we write that to be, why is equal to 3/4 X now? Our next line says in doubles toe 1 50 per therm. After 25. Our next line, our slope he's gonna double slope is one point five. So our line a look, something like this Why is equal to 1.5 x? Let's be now we don't know it be is a rough graph. Looks something like this will go up to 3/4 and then our slope will double go up there. Is there? Why durex? But we can figure out what this point is. And with that, we confined what are be intercept of our second Linus. That was something done here. So it's plugged in 25 into our first block. Appear when X is equal to 25. Let x 25. Why is equal to 25 3/4 and that becomes 75 4th I mean, at this point right here, point is equal to 25 75 4th That point must be on both lines so we can plug that in our second equation. So why is equal to 75 4th? She had a 1.5 excessive 25 plus B 25 times, 1.5 this 37 0.5 Must be when we do the math friend that be is equal to negative 18.75 The equation for a second line. I had to be wise. The 1.5 x minus 18 75 Because we're writing are piece wise function. We can say that see of X is equal to for the beginning. It's 3/4 x and that is one X is between zero and 25 for a second portion, he said it was 1.5 x point five x minus 18.75 and that is one X is greater than 25. I'm just plotted this in Desmond's as well, Jack in that Here. You see that yet that does agree our work. And now we're asked to check what is the value in 45 years when accessible to 45. So we're looking at sea of 45 therms. The 1.5 times 45 minus 18.75 comes out to 67.5, minus 18.75 48 points. You have 45 therms, $48 and 75 cents with under graph down with 45 therms. Would be We also found what are two different equations and are piece wise function of here. That is every thanks for watching.

In this problem I want to graph the piecewise function, I'm gonna start with the first piece negative three if X is less than or equal to negative two. So I'm gonna be working with negative two on my X axis here And it says it's gonna be at -3 at that point. So it's or equal to it's gonna be a closed circle and then everything less than that is just a horizontal line at the -3. The second piece X minus one. If negative two is less than X which is less than or equal to two. So I'm gonna be working between negative two and positive too. And if I was to start with the negative to um -2 -1, is that negative three and already have a point there. But in this part it's actually an open circle. So it's really important to pay attention to which piece we're looking at -1 -1 is -2, 0 -1 is negative one, 1 -1 is zero And 2 -1 is one. And this last one is going to be a closed point because it's X. is less than or equal to two. So I'm going to connect these and then the last piece is zero if X is greater than two, so I'm gonna go to exit two and zero and it's going to be an open circle because it is not or equal to and then it's gonna be a horizontal line for everything greater than that. It's kind of hard to see with the coloring but you can see the arrow and it is there. So this function or this piece wise function had three pieces and we have three pieces on the graph.


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