Determine the intervals on which the function is continuous

[Nicolas5150]

Homework Statement

Determine the intervals on which the function is continuous, support with graph.
15) f(x)=x^2+(5/x)

16) g(g)= 5-x, x<1
2x-3, x>1

17) f(x)=√(4/(x-8))

Homework Equations

The Attempt at a Solution

I understand the concept behind not being able to have 0/0. Therefore any breaks where x causes the denominator to equal zero would be a discontinuity in the graph.
Most of the problems I have done have had a polynomial where I could factor and then clearly see any denominator values that cause a zero.

15) for this problem I made x^2+(5/x) into (x^3 +5)/ x from here i am not sure where to go since the only thing i can see is that here x cannot equal zero or the denominator will cause a 0/0 effect
when I graph it as well I get an unusual graph as well

16) The only thing I can see to do would be plug in 1 for x resulting in 5-1 = 4 and 2*1-3=-1

17) Here I got rid of the square root by multiplying the function by itself to get 4/(x-8) With this i can visually see that x cannot equal 8. So possibly the intervals would be [8, infinity)

If anyone could help guide me in the right direction on how to approach the problems as well as confirm or deny 17 as being correct it would be greatly appreciated.

 

[haruspex]

15) the only thing i can see is that here x cannot equal zero

Exactly

16) The only thing I can see to do would be plug in 1 for x resulting in 5-1 = 4 and 2*1-3=-1

Right again. So your answer is?

17) Here I got rid of the square root by multiplying the function by itself to get 4/(x-8) With this i can visually see that x cannot equal 8. So possibly the intervals would be [8, infinity)

[8, infinity) includes 8 - you need to exclude it. There's also < 8.