Piecewise function

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Calc12

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For the function f(x) = { -3x + 2 if x < 1
{ x^2 if x > 1

a) sketch the piecewise function

b) determine the x-values, if any, at which the function is discontinuous. Find appropriate limits to support your conclusion.




Attached is my sketch, I don't know if it's correct?
I don't know how to do b.

Thank you in advanced.
 
Calc12 said:
For the function f(x) = { -3x + 2 if x < 1
{ x^2 if x > 1

a) sketch the piecewise function

b) determine the x-values, if any, at which the function is discontinuous. Find appropriate limits to support your conclusion.




Attached is my sketch, I don't know if it's correct?
I don't know how to do b.

Thank you in advanced.
Click to expand...

It should be very clear to you - where the function is discontinuous, from the graph that you presented.
 
Calc12 said:
I don't think my sketch it right

You're right; it's not.
Click to expand...

Do you remember y = mx + b ?

b is the y-intercept.

We have y = -3x + 2, for x < 1.

b = 2, not -2. Fix your y-intercept.

The slope m is -3. Lines with negative slope go "downhill" as we move from left to right. Your line goes "uphill". Fix that, too.

Lastly, don't continue the line beyond the open dot. The line "stops" at (1, -1).

Your graph for the x^2 part is okay at (1, 1), but it should go through (2, 4).

I mean, the curve is way off.

Are you really in a calculus class? I'm thinking that you might have posted your exercise on the wrong board.

For part (b), please tell us what you've learned about limits, so far.

Cheers ~ Mark

 
Thanks for the help.

I am taking Calculus and Vectors 12 for the first time, through corrospondance at home! There is no support material and textbooks, you guys and the internet is all I have!
I just started, this specific question is from Unit 1 - Lesson 2: Understanding Limits

I am still trying to comprehend what limits really are.
I know at x=1 it is discontinuous, but confused how to "support it"
 
Calc12 said:
Thanks for the help.
I know at x=1 it is discontinuous, but confused how to "support it"
Click to expand...

Try to answer the following question:

What property "must" a function have - so that it can defined continuous at a point?
 
What property "must" a function have - so that it can defined continuous at a point?


A limit?
 


Can you upload a correct graph, yet?

We can use it to address part (b).

 
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