20N.1.SL.TZ0.S_4

pestleMathematicsAASLPaper 120N· sl-2-9-exponential-and-logarithmic-functionssource ↗

Let $f (x) = a \log_{3} (x - 4)$ , for $x > 4$ , where $a > 0$ .

Point $A (13, 7)$ lies on the graph of $f$ .

Find the value of $a$ .

[3]

The $x$ -intercept of the graph of $f$ is $(5, 0)$ .

On the following grid, sketch the graph of $f$ .

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to substitute coordinates (in any order) into $f$ (M1)

eg $a \log_{3} (13 - 4) = 7, a \log_{3} (7 - 4) = 13, a \log 9 = 7$

finding $\log_{3} 9 = 2$ (seen anywhere) (A1)

eg $\log_{3} 9 = 2, 2 a = 7$

$a = \frac{7}{2}$ A1 N2

[3 marks]

A1A1A1 N3

Note: Award A1 for correct shape of logarithmic function (must be increasing and concave down).
Only if the shape is correct, award the following:
A1 for being asymptotic to $x = 4$
A1 for curve including both points in circles.

[3 marks]

Examiners’ report

[N/A]