Continuity of a piecewise function need help please!

[ada_beta]

g(x)=
C/(x-17) if x<10
C +3x if x=10
2C -4 if x>10

Find the value for C that makes the function continuous on (-infinity,10]

And is it possible to find a value for C that makes this function continuous over (-infinity, infinity) ?

I know how to solve this if it only had two pieces in the function and asking for it to be continuous from (-infinity, infinity) by finding the limit of each piece of it to 10 and setting them equal to each other to find C.

BUT

there are three components to this function! I don't know what to do...:-|

 

[daon2]

g(x)=
C/(x-17) if x<10
C +3x if x=10
2C -4 if x>10

Find the value for C that makes the function continuous on (-infinity,10]

And is it possible to find a value for C that makes this function continuous over (-infinity, infinity) ?

I know how to solve this if it only had two pieces in the function and asking for it to be continuous from (-infinity, infinity) by finding the limit of each piece of it to 10 and setting them equal to each other to find C.

BUT

there are three components to this function! I don't know what to do...:-|

The same thing! Answer the following:

The limit as x approaches 10 from the left, in terms of C is _____

The limit as x approaches 10 from the right, in terms of C is _____

The value of f(10) in terms of C is ______

In order for the function to be continuous we need that 1) the limit of f(x) exists for x→10, and 2) the limit equals f(10)

 

[ada_beta]

The same thing! Answer the following:

The limit as x approaches 10 from the left, in terms of C is _____

The limit as x approaches 10 from the right, in terms of C is _____

The value of f(10) in terms of C is ______

In order for the function to be continuous we need that 1) the limit of f(x) exists at x=10, and 2) the limit equals f(10)

Okay to answer the blanks

The same thing! Answer the following:

The limit as x approaches 10 from the left, in terms of C is ____ -(C/7)

The limit as x approaches 10 from the right, in terms of C is _____ 2C-4

The value of f(10) in terms of C is ______ C + 30

Assuming those terms are correct above do I just set the top two equal to each other and solve for C? The bottom two equal to each other? Or all three set equal to each other to solve for C? The more I look at this the more I think that there is no value for C for it to be continuous from (-infinity,infinity) only from (-infinity,10]

 

[daon2]

Okay to answer the blanks

The same thing! Answer the following:

The limit as x approaches 10 from the left, in terms of C is ____ -(C/7)

The limit as x approaches 10 from the right, in terms of C is _____ 2C-4

The value of f(10) in terms of C is ______ C + 30

Assuming those terms are correct above do I just set the top two equal to each other and solve for C? The bottom two equal to each other? Or all three set equal to each other to solve for C? The more I look at this the more I think that there is no value for C for it to be continuous from (-infinity,infinity) only from (-infinity,10]

I agree! There can only be one C which satisfies -C/7 = C+30. If that is not the same C which satisfies 2C-4=C+30, then f(x) cannot be continuous at x=10.

 

[ada_beta]

I agree! There can only be one C which satisfies -C/7 = C+30. If that is not the same C which satisfies 2C-4=C+30, then f(x) cannot be continuous at x=10.

Thank you so much!!! I got it and now I can pass this Lab Report with flying colors.