Match the following :

Column (A) — four graphs (a), (b), (c), (d) (each shown in the original paper).

Column (B):
(i) $f : \mathbb{R} o \mathbb{R}$ given by $f(x) = \dfrac{1}{x}, x
e 0$
(ii) $f : \mathbb{R} o \mathbb{R}$ given by $f(x) = x^3, x \in \mathbb{R}$
(iii) $f :

Question

Match the following :

Column (A) — four graphs (a), (b), (c), (d) (each shown in the original paper).

Column (B):
(i) $f : \mathbb{R} 	o \mathbb{R}$ given by $f(x) = \dfrac{1}{x}, x 
e 0$
(ii) $f : \mathbb{R} 	o \mathbb{R}$ given by $f(x) = x^3, x \in \mathbb{R}$
(iii) $f : \mathbb{R} 	o \mathbb{R}$ given by $f(x) = x, x \in \mathbb{R}$
(iv) $f : \mathbb{R} 	o \mathbb{R}$ given by $f(x) = \begin{cases} 1, & 	ext{if } x > 0 \ 0, & 	ext{if } x = 0 \ -1, & 	ext{if } x < 0 \end{cases}$
(v) $f : \mathbb{R} 	o \mathbb{R}$ given by $f(x) = |x|, x \in \mathbb{R}$

Match each graph in Column (A) with its corresponding function definition in Column (B).

Accepted Answer

> > [!TLDR] > Recognise each curve's shape: an S-shaped curve is the cube function, a two-level step is the piecewise sign-type function, a straight line through the origin at 45 degrees is the identity function, and a two-branch curve hugging the axes is the reciprocal function. > > - **Graph (a)** is a smooth, origin-symmetric S-shaped curve rising steeply -- this is the cubic $f(x)=x^3$, i.e. definition **(ii)**. > - **Graph (b)** is a two-level horizontal step, $y=1$ for $x>0$ and $y=-1$ for $x<0$ -- this matches the piecewise function equal to $1$ for $x>0$, $0$ at $x=0$, $-1$ for $x<0$, i.e. definition **(iv)**. > - **Graph (c)** is a straight line through the origin with slope $1$ -- the identity function $f(x)=x$, i.e. definition **(iii)**. …

Q.Match the following : Column (A) — four graphs (a), (b), (c),

Concept understanding — Representation and Graph of a Function

Q.Match the following : Column (A) — four graphs (a), (b), (c),

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