Question

PLEASE HELP
Identify holes in the graph of the function.
f(x)=(x^2+x−6)/(x−2)

hole at x = 2
hole at x = -2
hole at x = 1
hole at x = 0

Answer 1

@Directrix @zepdrix

Answer 2

A "hole" in a graph comes from a restriction in the domain.
The domain is the set of x-coordinates of a function.
If a function contains an expression with, for example, a variable in a denominator, or a square root containing a variable, you must restrict the domain to only allowed values.

Answer 3

Look at your function.

\(f(x) = \dfrac{x^2 + x - 6}{x - 2} \)

The function is a rational function, which means a fraction of a polynomial divided by a polynomial.

In the numerator, you can let x be any real number. There is no problem there.
Any real number you allow x to be can be used in the numerator, and it will evaluate to a real number.

Now look at the denominator.
First, is there a number that you cannot divide by?

Answer 4

Can you do the three divisions below?
If not, then which one can you not do and why?

Answer 5

You can do the first and second one but not the last because you can't divide 0

Answer 6

3/2 and 2/1