Mathematical Methods — Question 18

QCAA 2020, Paper 1 · 6 marks

Q18 · 2020 · Technology-freeComplex familiar6 marks

QUESTION 18 (6 marks)

The function

f(x)

has the form

f(x)=3\log_2(x+a)+b

. The function

g(x)

has the form

g(x)=-\log_3(x+c)+5

. A section of the graphs of the two functions is shown. Determine the values of

a

b

and

c

WORKED SOLUTION

6 marks

ANSWER

a=2

b=-2

c=1

Worked solution

Using the

y

-intercepts gives

1=3\log_2(a)+b

and

5=-\log_3(c)+5

, so

c=1

. Using the point of intersection

(2,4)

4=3\log_2(2+a)+b

. Solving the two equations in

a

and

b

gives

a=2

and

b=-2

correctly determines

c

[1 mark]

correctly establishes two equations in

a

and

b

[1 mark]

correctly selects procedure to solve for unknowns

[1 mark]

correctly determines

a

[1 mark]

determines

b

[1 mark]

shows logical organisation communicating key steps

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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