+845 https://snag.gy/qfoDxR.jpg
i need help on question 3D please explain each steps
+128406 y = [ x ( x - 2) ] / [ x^2 - 1 ] = [x^2 - 2x] / [ (x + 1) ( x - 1) ] = (x^2 - 2x) / [ x^2 - 1)
a) Setting both linear factors in the denominator to 0 and solving for x gives us the vertical asyptotes of x = -1 and x = 1
Because the coefficients on each of the x^2 terms in the numerator/ denominator are 1, their ratio gives the horizontal asymptote of y = 1 / 1 = 1
b) To see where it crosses the x axis, let y = 0 and we have
0 = x (x - 2) / (x^2 - 1) multiply both sides by x^2 - 1
0 = x ( x - 2) set both factors to 0 and solve for x and we get the x intercepts of x = 0 and x = 2
To see where it crosses the y axis, let x = 0 and we have 0 (0 - 2) / ( 0^2 - 1) = 0
c) Here is the curve : https://www.desmos.com/calculator/i0vbehvizi
d) Inspection of the graph reveals that the intervals that solve this inequality are (-infinity ,-1) U [0, 1) U [2, infinity )
+845 the final answer for D should be 𝑥 ≥ 2, 0 ≤ 𝑥 < 1, 𝑥 < −1
which is really confusing please explain
+128406 My notation means the same thing
x ≥ 2 is the same as [2, infinity )
x < -1 is the same as ( - infinity, -1)
0 ≤ 𝑥 < 1 is the same as [0, -1 )
+845 sorry but can u please explain how u get those values as im really bad at graphs
+128406 OK...look at the graph....
Note that the graph is above y = 0 from x = -infinity to x = - 1 [but not including -1 ]
And the graph is equal to or above y = 0 from x = 0 0 to x = 1 [ icluding 0, but not including 1]
Ad the graph is equal to or above y = 0 from x = 2 to x = infinity [ including 2 ]
