We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Rational function

0
223
6
+846

https://snag.gy/qfoDxR.jpg

i need help on question 3D please explain each steps

Sep 29, 2018

### 6+0 Answers

#1
+101870
+2

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 )

Sep 29, 2018
#2
+846
+1

the final answer for D should be 𝑥 ≥ 2, 0 ≤ 𝑥 < 1, 𝑥 < −1

which is really confusing please explain

YEEEEEET  Sep 29, 2018
#3
+101870
+2

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 )

CPhill  Sep 29, 2018
#4
+846
+1

sorry but can u please explain how u get those values as im really bad at graphs

YEEEEEET  Sep 29, 2018
#5
+101870
+2

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 ]

CPhill  Sep 29, 2018
#6
+846
+1

thank you so much!

YEEEEEET  Sep 29, 2018