Plot the graph of the following functions using GeoGebra Graphing calculator:

a) $f(x) = x^2$

b) $f(x) = x^3$

c) $f(x) = 1/x$

Question

Plot the graph of the following functions using GeoGebra Graphing calculator:

a) $f(x) = x^2$

b) $f(x) = x^3$

c) $f(x) = 1/x$

Accepted Answer

> [!TLDR]
> This is a GeoGebra graphing activity — plot each function point-by-point (or by typing it directly into GeoGebra's input bar) and record its key shape features.

> [!FORMULA]
> To plot a function $y=f(x)$ in GeoGebra: type `f(x)=x^2`, `f(x)=x^3`, `f(x)=1/x` (one at a time or as $f,g,h$) into the Input bar and press Enter; GeoGebra auto-draws the curve. By hand, tabulate $y=f(x)$ for several $x$ and join the points smoothly.

1. **(a) $f(x)=x^2$.** Build a table of values:

| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
   |---|---|---|---|---|---|
   | $y$ | $4$ | $1$ | $0$ | $1$ | $4$ |

Plotting these points gives an **upward-opening parabola** with vertex at the origin $(0,0)$, symmetric about the $y$-axis (since $f(-x)=f(x)$, it is an **even** function). Domain $=\mathbb{R}$, range $=[0,\infty)$.

2. **(b) $f(x)=x^3$.**

| $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
   |---|---|---|---|---|---|
   | $y$ | $-8$ | $-1$ | $0$ | $1$ | $8$ |

Plotting gives an **S-shaped (odd) curve** through the origin, symmetric about the origin ($f(-x)=-f(x)$), increasing everywhere, with an inflection/flattening at $x=0$. Domain $=\mathbb{R}$, range $=\mathbb{R}$.

3. **(c) $f(x)=1/x$.**

| $x$ | $-2$ | $-1$ | $-0.5$ | $0.5$ | $1$ | $2$ |
   |---|---|---|---|---|---|---|
   | $y$ | $-0.5$ | $-1$ | $-2$ | $2$ | $1$ | $0.5$ | …

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