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Date May 2022 Marks available 1 Reference code 22M.1.SL.TZ2.4
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Write down Question number 4 Adapted from N/A

Question

A function f is defined by fx=2x-1x+1, where x, x-1.

The graph of y=f(x) has a vertical asymptote and a horizontal asymptote.

Write down the equation of the vertical asymptote.

[1]
a.i.

Write down the equation of the horizontal asymptote.

[1]
a.ii.

On the set of axes below, sketch the graph of y=f(x).

On your sketch, clearly indicate the asymptotes and the position of any points of intersection with the axes.

[3]
b.

Hence, solve the inequality 0<2x-1x+1<2.

[1]
c.

Markscheme

x=-1          A1

 

[1 mark]

a.i.

y=2          A1

 

[1 mark]

a.ii.

 

rational function shape with two branches in opposite quadrants, with two correctly positioned asymptotes and asymptotic behaviour shown         A1

 

Note: The equations of the asymptotes are not required on the graph provided there is a clear indication of asymptotic behaviour at x=-1 and y=2 (or at their FT asymptotes from part (a)).

 

axes intercepts clearly shown at x=12 and y=-1         A1A1

 

[3 marks]

b.

x>12         A1

 

Note: Accept correct alternative correct notation, such as 12,  and ]12,[.

 

[1 mark]

c.

Examiners report

It is pleasing to note that many candidates were familiar with the shape of the graph of a rational function of the form f(x)=ax+bcx+d, and a large number of them were able to sketch an appropriate graph. Part (c) was a struggle for the majority of candidates, with only a few answering correctly. Despite the word "hence" and the single mark available in this part, most candidates who attempted part (c) did so by trying to solve the inequality algebraically, rather than seeing the connection to the values in their graph.

a.i.
[N/A]
a.ii.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.3—Graphing
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