CAIE IGCSE Additional Math 1.8 Sketch Functions and Inverses Questions

Practise Cambridge IGCSE Additional Mathematics by reflecting function graphs in y=x, identifying intercepts and solving fixed-point relationships.

Exam points

Sketch the graphs of a function and its inverse as reflections in the line y=x.
Use intercepts, intersections and symmetry to interpret relationships between f(x) and f⁻¹(x).
Solve or identify fixed points where a function meets its inverse or the line y=x.

[Maximum number: 5]

function f is such that $\mathrm{f}(x)=2 x^{2}+5 x+3$ , for $x \geqslant p$ , where p is a constant.
It is given that $\mathrm{f}^{-1}$ exists.

Using your value of p, sketch the graphs of $y=\mathrm{f}(x)$ and $y=\mathrm{f}^{-1}(x)$ .
Label each graph.
State the intercepts of each of the graphs with the axes.

Figure for Question CAIE IGCSE Additional Math 1.8 Sketch Functions and Inverses Questions question 1 — CAIE IGCSE Additional Math

Figure for Answer to Question CAIE IGCSE Additional Math 1.8 Sketch Functions and Inverses Questions question 1 — CAIE IGCSE Additional Math

B1 for $y=\mathrm{f}(x)$ drawn as a one-one function in the first, second and third quadrants or first and second quadrants.

Must have correct curvature

Dep B1 for $y=\mathrm{f}^{-1}(x)$ as a reflection of their $y=\mathrm{f}(x)$ in the line y=x. Maybe implied by intercepts, but must have the correct curvature

B1 for $y=\mathrm{f}(x)$ clearly passing through x=-1 correctly soi. Allow if domain is unrestricted but must have correct quadratic shape or curvature

B1 for $y=\mathrm{f}(x)$ passing through y=3 only on the y-axis soi. Allow if domain is unrestricted but must have correct quadratic shape or curvature

B1 for - 1 and 3 marked correctly for $y=\mathrm{f}^{-1}(x)$ allow for unrestricted range.

Must have correct curvature.

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CAIE IGCSE Additional Math 1.8 Sketch Functions and Inverses Questions question 1