Question

Where is the removable discontinuity of f (x) = StartFraction x + 5 Over x squared + 3 x minus 10 EndFraction located?
x = –5
x = –2
x = 2
x = 5
This is a pre-calculus question for grade 12 I just need some help!

Answer 1

A removal discontinuity can be defined as a point on a graph that is undefined.
They can exist if there is a blip in the function
Or if there is a common factor within the denominator/numerator, in your case:
\[\Large f(x) = \frac{ x+5}{x^2+3x-10}\]
can be factored into:
\[\Large f(x) =\frac{x+5}{(x+5)(x-2)}\]

As you can see, there is a common factor of x+5

You just gotta set this equal to 0 to find the point of discontinuity:
\[\large x+5 =0 \]