19M.1.SL.TZ2.S_4

pestleMathematicsAISLPaper 119M· ahl-2-8-transformations-of-graphs-composite-transformationssource ↗

The following diagram shows part of the graph of $f$ with $x$ -intercept (5, 0) and $y$ -intercept (0, 8).

Find the $y$ -intercept of the graph of $f\left( x \right) + 3$ .

[1]

a.i.

Find the $y$ -intercept of the graph of $f\left( {4x} \right)$ .

[2]

a.ii.

Find the $x$ -intercept of the graph of $f\left( {2x} \right)$ .

[2]

Describe the transformation $f\left( {x + 1} \right)$ .

[2]

Markscheme / solution

$y$ -intercept is 11 (accept (0, 11) ) A1 N1

[1 mark]

a.i.

valid approach (M1)

eg $f\left( {4 \times 0} \right) = f\left( 0 \right)$ , recognizing stretch of $\frac{1}{4}$ in $x$ -direction

$y$ -intercept is 8 (accept (0, 8) ) A1 N2

[2 marks]

a.ii.

$x$ -intercept is $\frac{5}{2}\,\,\left( { = 2.5} \right)$ (accept $\left( {\frac{5}{2}{\text{,}}\,\,\,0} \right)$ or (2.5, 0) ) A2 N2

[2 marks]

correct name, correct magnitude and direction A1A1 N2

eg name: translation, (horizontal) shift (do not accept move)

eg magnitude and direction: 1 unit to the left, $\left( {\begin{array}{*{20}{c}} { - 1} \\ 0 \end{array}} \right)$ , horizontal by –1

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]