smc-1073-30-Other

Functions, EXT1 F1 2022 HSC 4 MC

The diagram shows the graph of the sum of the functions `f(x)` and `g(x)`.

Which of the following best represents the graphs of both `f(x)` and `g(x)`?

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`A`

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`text{By Elimination,}`

`text{Consider the}\ ytext{-intersection of both graphs in each option:}`

`B and C\ text{will have result in a positive}\ ytext{-intersection (Eliminate)}`

`y=f(x)+g(x)=0\ \ text{when the two graphs are equidistant from}`

`text{the}\ xtext{-axis (Eliminate}\ D).`

`=>A`

The diagram shows the graph of the function `f(x) = x/(x - 1)`.

If `g(x)=x`, draw a separate half-page graph of `y = f(x) + g(x)` (2 marks)

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`text(As)\ x -> ∞, \ y -> x + 1`

♦ Mean mark part (iii) 49%.

`text(As)\ x -> – ∞, \ y -> x + 1`

The diagram shows the graph of `y =f(x)`. The graph has a horizontal asymptote at `y =2`.

Draw separate one-third page sketches of the graphs of the following:

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ii.

iii.

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ii.

iii.

Which graph best represents the curve `y = (x - 1)^2 (x + 3)^5?`

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`A`

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`text(Quick elimination)`

`text(At)\ \ x=0,\ \ y>0\ \ \ \ =>\ text{NOT (B) or (C)}`

`(x – 1)^2\ \ text(gives a turning point at)\ \ x = 1,`

`(x + 3)^5\ \ text(gives a change in concavity at)\ \ x = -3.`

`=> A`

The diagram shows the graph `y = (x(2x − 3))/(x − 1)`. The line `l` is an asymptote.

Use the above graph to draw a sketch of the graph

`y = (x − 1)/(x(2x − 3))`

indicating all asymptotes and all `x`- and `y`-intercepts. (2 marks)

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Write `(x(2x − 3))/(x − 1)` in the form `mx + b + a/(x − 1)`. (1 mark)

--- 3 WORK AREA LINES (style=lined) ---

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