+15 I got a quiz back and I didn't understand why I missed a question. The teacher explained it, something like "we read range from the bottom to the top," but I still don't understand it.
Here's the equation: f(x)=(2x3+5x2-3x)/(x2-x)
I got the range to be (-inf, 3.343] U [14.657, inf) using my graphing calculator.
She said that the range was (-inf, 3) U (3, 3.343] U [14.657, inf).
Now, don't get me wrong, I know there's a hole at (0, 3), but I thought that since there was another point where it crossed the y-axis, being (-1, 3), that 3 would be a valid value of the range.
Who's right and who's wrong? If my teacher is right can someone give me an explanation or a helpful video or something?
Thanks!
+128475 (2x^3 + 5x^2 - 3x)
f(x) = ______________ =
x^2 - x
x (2x^2 + 5x - 3)
______________ =
x (x - 1)
2x^2 + 5x - 3
___________ =
x - 1
(2x - 1) ( x + 3)
____________
x - 1
We have a "hole" at x = 0 and a vertical asymptote at x = 1
We also have a "slant" asymptote determined as follows :
2x + 7
x^2 - x [ 2x^3 + 5x^2 - 3x ]
2x^3 - 2x^2
________________
7x^2 - 3x
7x^2 - 7x
__________
So.....the slant asymptote is y = 2x + 7
The range is (-inf, 3.343] U [ 14.657, inf)
Note that the graph crosses the line y = 3.....so......it definitely exists when y = 3
See the graph here : https://www.desmos.com/calculator/e5di4axkpw
