SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Functions, 2ADV’ F2 2019 HSC 4 MC

′

The diagram shows the graph of  `y = f(x)`.
 


 

Which equation best describes the graph?

A.     `y = x/(x^2 - 1)`

B.     `y = x^2/(x^2 - 1)`

C.     `y = x/(1 - x^2)`

D.     `y = x^2/(1 - x^2)`

Show Answers Only

`B`

Show Worked Solution

`text(By elimination:)`

`text(Graph is an even function)`

`=> f(x) = f(-x)`

`:.\ text(Eliminate A and C)`
 

`text(When)\ -1 < x < 1,\ \ y <= 0`

`:.\ text(Eliminate D)`

`=>  B`

Functions, 2ADV’ F2 2017 HSC 5 MC

Which graph best represents the function  `y = (2x^2)/(1-x^2)`?
 

A. B.
       
C. D.
Show Answers Only

`D`

Show Worked Solution
`y` `= (2x^2)/((1-x^2))`
  `= −((2-2x^2-2))/((1-x^2))`
  `= −(2(1-x^2))/((1-x^2))-2/((1-x^2))`
  `= −2-2/((1-x^2))`

 

`text(As)\ \ x -> oo,\ \ y -> −2`

`:. text(Horizontal asymptote at)\ \ y = −2`

`⇒D`