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L&E, 2ADV E1 2021 HSC 5 MC

Which of the following best represents the graph of  `y = 10 (0.8)^x`?
 

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`A`

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`\text{By elimination:}`

`\text{When} \ x = 0 \ , \ y = 10(0.8) ^0 = 10`

`-> \ text{Eliminate B and D}`

`text(As)\ \ x→oo, \ y→0`

`-> \ text{Eliminate C}`

`=> A`

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)`

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`B`

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`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.
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`D`

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`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`