SOLUTION: Are the functions continuous? Determine whether f is continuous at c. Use algebraic substitution, graphing, and or tables to determine. 3. f(x) = (x+3)/(x-3), c = 3 4.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Are the functions continuous? Determine whether f is continuous at c. Use algebraic substitution, graphing, and or tables to determine. 3. f(x) = (x+3)/(x-3), c = 3 4.      Log On

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Question 1139411: Are the functions continuous?
Determine whether f is continuous at c. Use algebraic substitution, graphing, and or tables to determine.
3. f(x) = (x+3)/(x-3), c = 3

4. f(x) = (x^2 + 3x)/(x^2 - 3x), c = 0
I think they are both not continuous but im not sure.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3. f%28x%29+=+%28x%2B3%29%2F%28x-3%29, c+=+3
if+c is of the given value for+x
f%283%29+=+%283%2B3%29%2F%283-3%29=6%2F0-> undefined
4. f%28x%29+=+%28x%5E2+%2B+3x%29%2F%28x%5E2+-+3x%29, c+=+0+
f%280%29+=+%280%5E2+%2B+3%2A0%29%2F%280%5E2+-+3%2A0%29=0%2F0->+undefined
In both examples 3. and 4. if c is of the given value for x, the DENOMINATOR of the function becomes ZERO which is undefined. Thus the function has a 'hole ' there and is not continuous.