Mathematical Methods — Question 4

QCAA 2020, Paper 2 · 1 mark

Q4 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 4

Consider the function

f(x)=\log_p(x+q)

where

p>1

and

0<q<1

. Which of the following could be the graph of

f(x)

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

Because

p>1

, the graph is increasing. Its vertical asymptote is

x=-q

, which lies between

-1

and

0

, and its

x

-intercept is

x=1-q

, between

0

and

1

. Only option C has these features.

Selects option C.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.