Calculus graphing with conditions

[algray09]

I’m confused on how to graph these conditions like where do I start?

 

[Deleted member 4993]

I’m confused on how to graph these conditions like where do I start?

This problem gives you almost step-by-step instructions.
Where do you start by plotting the two points described in the first condition provided.

 

[algray09]

I get the first part now and I know what to do when given one interval but having trouble with the multiple intervals

 

[Deleted member 4993]

I get the first part now and I know what to do when given one interval but having trouble with the multiple intervals

Please post an image of your work.

 

[algray09]

What I’ve done so far, the reason I’m having trouble is because my teacher briefly talked about it in class and went straight into polynomial functions the rest of class. Do I make a continuous line for the intervals? The intervals is what I’m more confused on

 

[Deleted member 4993]

What I’ve done so far, the reason I’m having trouble is because my teacher briefly talked about it in class and went straight into polynomial functions the rest of class. Do I make a continuous line for the intervals? The intervals is what I’m more confused on

Which is your x-axis?

Which is your y-axis?

You drew: where are the two points (-3,-1) & (0,0) for condition # 1

 

[algray09]

I figured it out

 

[Deleted member 4993]

I figured it out

I am afraid that that graph does not satisfy the condition(1)

 

[algray09]

I don’t know how else to draw it then because it is concave up and concave down in the spots that it says to. It increases and decreases in the spots that it says too. Unless the -3 is where the concave up is then I’ll make it that but I asked how someone from class drew it and they were confused too but got that shape. I was more confused on the interval parts but they helped me out.

 

[Steven G]

If you lower the entire graph or raise the x-axis, then you will have satisfied condition 1.

 

[Dr.Peterson]

I don’t know how else to draw it then because it is concave up and concave down in the spots that it says to. It increases and decreases in the spots that it says too. Unless the -3 is where the concave up is then I’ll make it that but I asked how someone from class drew it and they were confused too but got that shape. I was more confused on the interval parts but they helped me out.

It may help if I describe what you drew, so you can see how it differs from what it should be.

Here is what you were told:

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Here is your sketch:

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Here is my description:

• [imath]f(-1) = 1, f(0) = 2[/imath]; both are wrong. You made a dot at (0,0), but didn't use it for the curve. You didn't even make a dot at (-1,-3), but have one at (0,-3).
• [imath]f(x)[/imath] is increasing on [imath](-\infty,-3.5), (-1.5,0), (2,\infty)[/imath]; these are similar to what was asked, but the numbers are wrong. I have to add that your axes are so irregular that it is hard to tell what you intended. The ticks should be spaced regularly.
• [imath]f(x)[/imath] is decreasing on [imath](-3.5,-1.5), (0,2)[/imath]
• [imath]f(x)[/imath] is concave up never; it is linear (constant slope, no concavity) on three segments. You need more curves.
• [imath]f(x)[/imath] is concave down on [imath](-1,1.5)[/imath]
• As [imath]x\to\infty, f(x)\to\infty[/imath]; correct.
• As [imath]x\to-\infty, f(x)\to-\infty[/imath]; correct. But you should have arrows on the ends to show this.

If you tell us why you think it fits the description, we may be able to see what you are misunderstanding. I think, for one thing, you are not clear on interval notation; and possibly also on the coordinates of points.