Question

Determine where each of the following functions is continuous.

Answer 1

The simple definition of continuous:
You could draw the function without lifting your pencil.

Answer 2

i.\[y=x^3-4x^2+2x-5\]
ii. \[f(x)=x^2-16 \div 2x^2+5x+3\]

Answer 3

Check if there are any holes.

Answer 4

@lalaly

Answer 5

@GoldRush18 why did you just ignore SmoothmMath?
that's quite rude, and I assure you that he can help you if you will only work with him

Answer 6

im sorry but i didn't understand what he meant

Answer 7

then you could ask him to explain
I do believe he's asking you if there are any values of x in these functions which for which they are are undefined

Answer 8

i.e. what are the domains of these functions?

Answer 9

just as how i posted them thats how it is on the question paper

Answer 10

i didn't understand them myself

Answer 11

okay, so to answer the question you need to know at what points these functions are undefined

Answer 12

do you know that domain of the first function you posted?

Answer 13

the domain*

Answer 14

no i don't

Answer 15

The domain means the inputs, or the xs. Most x inputs work just fine, but the ones that don't are the ones that make me divide by 0.
Simple example:

f(x) = 5/x
the domain is everything but x=0 because if I plug in 0, the denominator is 0. =(

Answer 16

things that make a function undefined include (but are not limited to):

division by zero
a square root of a negative number
a logarithm of zero, or a negative number

for the first function, is there any value of x that we could put in that will lead to one of the three things above?

Answer 17

they did not give any x value so i really don't know