Discontinuity/Continuity and piece-wise functions

[f(x)'s]

Problem:

F(x)={x^2-2x-15/x-5 if x (cannot equal) 5
{10 if x = 5

state the value of x for which the function is discontinuous and state the continuity conditions that are not satisfied.

Situation:

I don't understand how I can find where it is discontinous... Do I need to create a table when x approaches 5 from the right and when x approaches 5 from the left for the two conditions?! How do I know when it is continous and discontinous?

 

[pka]

Re: Discontinuity/Continuity

I don't understand how I can find where it is discontinous... Do I need to create a table when x approaches 5 from the right and when x approaches 5 from the left for the two conditions?! How do I know when it is continous and discontinous?

What are the conditions for continuity?

\(\displaystyle \L
\begin{array}{l}
F(x) = \left\{ \begin{array}{cc}
\frac{{x^2 - 2x - 15}}{{x - 5}}, & x\not= 5 \\
10, & x = 5 \\
\end{array} \right. \\
\lim _{x \to 5^ + } F(x) = \lim _{x \to 5^ - } F(x) = 8 \\
\end{array}\)

 

[f(x)'s]

Does that mean that this function is continuous at 8 and never discontinous?!

 

[stapel]

Assuming you mean "x^2-2x-15/x-5" to be "(x² - 2x - 15)/(x - 5)", then think about what you know about rational functions. Where are rational functions discontinuous? If they have any "gaps", what causes them?

Does this particular rational function have any "gaps"? If not, does "f(5) = 10" fit into the rest of the line? If so, does "f(5) = 10" fill that gap?

Hint: Try factoring the numerator of the rational expression. When you cancel, what do you get? How does the point (5, 10) relate to this?

Eliz.

 

[f(x)'s]

Thank you - I'll give that a shot!