CAIE IGCSE Mathematics Extended Function Graph Questions

Practise completing tables, plotting smooth cubic or related curves and drawing auxiliary lines to solve equations from intersections.

Syllabus
2028–2030
Topic
E2.10
Level
Extended

Exam points

  • substitute the listed x-values to complete a function table accurately before plotting
  • plot sufficient points and join them with a smooth curve over the required interval
  • rearrange an equation to derive a straight or horizontal line and read every intersection root

Covered syllabus points

E2.10.1 Draw and interpret function graphsE2.10.2 Solve equations graphicallyE2.10.3 Exponential growth and decay graphs

E2.10 Graphs of functions question 1

[Maximum number: 3]

Question (a)

(a)

The diagram shows the graph of y=f(x) for −1.5⩽x⩽5-1.5\leqslant x\leqslant5.

[ 3 ]

Question (i)

(i)

Find f(2).

[ 1 ]

Question (ii)

(ii)

Solve the equation f(x)=0 for −1.5⩽x⩽5-1.5\leqslant x\leqslant5.
x= or x= or x=

Question (iii)

(iii)

On the grid, draw a line y=mx so that f(x)=mx has exactly one solution for −1.5⩽x⩽5-1.5\leqslant x\leqslant5.

[ 2 ]
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