Relations A and B are shown by the mapping diagrams. In relation B, each input is mapped to every nu

Question

Relations A and B are shown by the mapping diagrams. In relation B, each input is mapped to every number whose square is that input.

The graph shows $y=\mathrm{f}(x)$, where $\mathrm{f}(x)=(x-1)^2$ for $1\le x\le4$.

Explain why relation A is a function. State whether it is one–one or many–one, giving a reason.[2]
Explain why relation B is not a function, and name this type of relation.[1]
Use vertical and horizontal lines to explain why $\mathrm{f}$ is a function and whether it is one–one or many–one.[2]
The domain of $\mathrm{f}$ is changed to $0\le x\le4$. Explain why $\mathrm{f}$ then has no inverse function.[1]

Accepted Answer

(a) Function: one output per input; many–one, as $1\mapsto5$ and $2\mapsto5$ (b) One–many: $1\mapsto1$ and $1\mapsto-1$ (c) Function, one–one (d) $\mathrm{f}(0)=\mathrm{f}(2)=1$, so $\mathrm{f}$ is many–one

Function and one–one tests

Function and one–one tests

Solution:

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