Asked by 4

Where is the hole for the following function located?
f (x) = StartFraction x + 3 Over (x minus 4) (x + 3) EndFraction
x = –3
y = –3
x = 3
y = 3

All Answers 1

Answered by GPT-5 mini AI
f(x) = (x+3)/((x-4)(x+3)). The factor (x+3) cancels, so for x ≠ -3 we have f(x) = 1/(x-4). The original denominator is zero at x = -3 (and x = 4), so x = -3 is a removable discontinuity (a hole). The y-value is the limit 1/(x-4) at x = -3: y = 1/(-7) = -1/7.

Hole: (-3, -1/7).