HW HELP PLZ!! The graph of the equation of the equation x^2 + 3x - 10 / x - 2 is a line with a hole in it. The hole occurs at the point??
2006-10-09 15:54:56 · 6 answers · asked by sportsrlife 1 in Science & Mathematics ➔ Mathematics
A graph does not exist where there is an unidentified answer, so that point is represented with an open circle in the graph. in this equation, the graph does not exist where the denominator equals zero. so to find this point, set the denominator equal to zero.
x-2=0
x=2
So the unidentified answer occurs at x=2
if you need to find the point, you need to factor the top into (x+5) and (x-2) then cancel out the (x-2) from both the top and the bottom to remove the discontinuity and plug in 2 for x.
(2)+5=7
so the point of discontinuity is (2,7)
2006-10-09 16:14:26 · answer #1 · answered by guy198 2 · 0⤊ 0⤋
The first thing you must know in mathematics is that when a number is coupled with a denominator that equals to 0, the overall answer is undefined.
In your graph for the equation (x^2 + 3x - 10)/(x -2), such a situations occurs when x = 2. This is due to the fact that 2 - 2 = 0, and the value of y at that point is undefined. Thus there is a "hole".
To find the exact point where the "hole" occurs, substitute x = 2 into the rest of the equation. This will give (2)^2 + 3(2) - 10 which gives you 0.
Thus the "hole" occurs at (2,0).
Hope that helps.
2006-10-10 03:39:26 · answer #2 · answered by xxmizuraxx 2 · 0⤊ 0⤋
x=2 will produce a hole in the graph. Look at the points of discontinuity. Think about a numerator and denominator of your function. Anytime the denominator is equal to zero, the function will be undefined. When will your function be undefined? The denominator will be equal to zero when x=2. 2-2 is equal to zero. Regardless of what the numerator is, the denominator is still zero!
2006-10-09 22:58:44 · answer #3 · answered by jessie03522 2 · 0⤊ 0⤋
The function is discontinuous at x = 0, obviously. The hole occurs at that point.
2006-10-09 23:01:02 · answer #4 · answered by Seshagiri 3 · 0⤊ 0⤋
since x = 2 will make this problem undefined, the point would be
2^2 + 3(2) - 10 = 4 + 6 - 10 = 10 - 10 = 0
ANS : (2,0)
2006-10-10 00:32:08 · answer #5 · answered by Sherman81 6 · 0⤊ 0⤋
the point where the denominator of that fraction will = 0.
2006-10-09 23:03:30 · answer #6 · answered by dan 4 · 0⤊ 0⤋