SOLUTION: Graph the rational equation {{{f(x)=((x^2)-25)/(x-5)}}} a. What do you notice about the graph at x = 5? b. Use the graph to estimate the limit as x approaches 5. c. What do

Algebra ->  Graphs -> SOLUTION: Graph the rational equation {{{f(x)=((x^2)-25)/(x-5)}}} a. What do you notice about the graph at x = 5? b. Use the graph to estimate the limit as x approaches 5. c. What do      Log On


   

Question 825669: Graph the rational equation f%28x%29=%28%28x%5E2%29-25%29%2F%28x-5%29
a. What do you notice about the graph at x = 5?
b. Use the graph to estimate the limit as x approaches 5.
c. What do you think is the correlation between a graph and a limit?
Found 3 solutions by Edwin McCravy, math-vortex, stanbon:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the rational equation %22f%28x%29%22%22%22=%22%22%28x%5E2-25%29%2F%28x-5%29

a. What do you notice about the graph at x = 5?
The equation is undefined at x=5, as cross%280%2F0%29 is not defined.

cross%28%22f%285%29%22=%285%5E2-25%29%2F%285-5%29=%2825-25%29%2F%285-5%29=0%2F0%29

That's why there is a hole in the graph, indicated by the
open circle.

b. Use the graph to estimate the limit as x approaches 5.
We can see that as x approaches 5 the value of y approaches 10, and we
write matrix%282%2C1%2Clim%2C%22x-%3E5%22%29%28%28x%5E2-25%29%2F%28x-5%29%29%22%22=%22%2210.

c. What do you think is the correlation between a graph and a limit?
That's a very vague question.  I'm guessing that what it's asking is that for
the graph of f(x) to be continuous at x=a, this must be true

matrix%282%2C1%2Clim%2C%22x-%3Ea%22%29%28%22f%28x%29%22%29%22%22=%22%22%22f%28a%29%22.

Edwin

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

Edwin gave a nice explanation for what's going on with this rational function. 

I'm actually very curious to now how you would answer question (c). 
c. What do you think is the correlation between a graph and a limit?


If you have questions about this, feel free email me through the algebra.com tutor link for this problem.

Hope this helps!
Mrs. Figgy
math.in.the.vortex@gmail.com

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Graph the rational equation f%28x%29=%28%28x%5E2%29-25%29%2F%28x-5%29
----
graph%28400%2C400%2C-10%2C10%2C-10%2C20%2C%28x%5E2-25%29%2F%28x-5%29%29
---------
a. What do you notice about the graph at x = 5?
f(5) is undefined.
--------------------------
b. Use the graph to estimate the limit as x approaches 5.
As x approaches 5, y approches 10.
---------------------------
c. What do you think is the correlation between a graph and a limit?
I'll leave that to you.
==============
Cheers,
Stan H.