91Ó°ÊÓ

The equation given is $y=x^2$. We need to sketch the graph and label three points on it.

Substituting the points $x=-1,0,1$on the graph we get,

when $x=-1$,

localid="1646388625228">y=x2⇒y=(-1)2⇒y=1

when $x=0$,

$$\begin{gathered} y=x^2 \\ ⇒y={\left(0\right)}^2 \\ ⇒y=0 \end{gathered}$$

when $x=1$,

$$\begin{gathered} y=x^2 \\ ⇒y={\left(1\right)}^2 \\ ⇒y=1 \end{gathered}$$

The points on the graph are $(-1,1),(0,0),(1,1)$.

The graph of the equation is:

The equation given is $y=x^3$. We need to sketch the graph and label three points on it.

Substituting the points $x=-1,0,1$on the graph we get,

when $x=-1$,

localid="1646389159712">y=x3⇒y=(-1)3⇒y=-1

when $x=0$,

localid="1646389218405">y=x3⇒y=(0)3⇒y=0

when $x=1$,

$$\begin{gathered} y=x^3 \\ ⇒y={\left(1\right)}^3 \\ ⇒y=1 \end{gathered}$$

The points on the graph are $(-1,-1),(0,0),(1,1)$.

The graph of the equation is:

The equation given is $y=e^x$. We need to sketch the graph and label three points on it.

Substituting the points $x=-1,0,1$on the graph we get,

when $x=-1$

$$\begin{gathered} y=e^x \\ ⇒y=e^{-1} \\ ⇒y=\frac{1}{e} \end{gathered}$$

when $x=0$

$$\begin{gathered} y=e^x \\ ⇒y=e^0 \\ ⇒y=1 \end{gathered}$$

when $x=1$,

$$\begin{gathered} y=e^x \\ ⇒y=e^1 \\ ⇒y=e \end{gathered}$$

The points on the graph are $\left(-1,\frac{1}{e}\right),(0,1),(1,e)$.

The graph of the equation is:

The equation given is $y=\ln x$. We need to sketch the graph and label three points on it.

The equation can also be written as:

$$\begin{gathered} y=\ln x \\ ⇒x=e^y \end{gathered}$$

Substituting the points $y=-1,0,1$on the graph we get,

when $y=-1$,

$$\begin{gathered} x=e^y \\ ⇒x=e^{-1} \\ ⇒x=\frac{1}{e} \end{gathered}$$

when localid="1646390422462">y=0,

$$\begin{gathered} x=e^y \\ ⇒x=e^0 \\ ⇒x=1 \end{gathered}$$

when $y=1$,

$$\begin{gathered} x=e^y \\ ⇒x=e^1 \\ ⇒x=e \end{gathered}$$

The points on the graph are $\left(\frac{1}{e},-1\right),(1,0),(e,1)$.

The graph of the equation is:

The equation given is $y=\sin x$. We need to sketch the graph and label three points on it.

Substituting the values of $x=-\frac{\mathrm{Ï€}}{2},0,\frac{\mathrm{Ï€}}{2}$we get,

when $x=-\frac{\mathrm{Ï€}}{2}$

$$\begin{gathered} y=\sin x \\ ⇒y=\sin \left(-\frac{\mathrm{π}}{2}\right) \\ ⇒y=-1 \end{gathered}$$

when $x=0$,

$$\begin{gathered} y=\sin x \\ ⇒y=\sin \left(0\right) \\ ⇒y=0 \end{gathered}$$

when $x=\frac{\mathrm{Ï€}}{2}$

$$\begin{gathered} y=\sin x \\ ⇒y=\sin \left(\frac{\mathrm{π}}{2}\right) \\ ⇒y=1 \end{gathered}$$

The points on the graph are $\left(-\frac{\mathrm{Ï€}}{2},-1\right),(0,0),\left(\frac{\mathrm{Ï€}}{2},1\right)$.

The graph of the function is:

The equation given is $y=\tan x$. We need to sketch the graph and label three points on it.

Substituting the values of $x=-\frac{\mathrm{Ï€}}{4},0,\frac{\mathrm{Ï€}}{4}$on the graph we get,

when $x=-\frac{\mathrm{Ï€}}{4}$,

$$\begin{gathered} y=\tan x \\ ⇒y=\tan \left(-\frac{\mathrm{π}}{4}\right) \\ ⇒y=-1 \end{gathered}$$

when $x=0$,

$$\begin{gathered} y=\tan x \\ ⇒y=\tan \left(0\right) \\ ⇒y=0 \end{gathered}$$

when $x=\frac{\mathrm{Ï€}}{4}$,

$$\begin{gathered} y=\tan x \\ ⇒y=\tan \left(\frac{\mathrm{π}}{4}\right) \\ ⇒y=1 \end{gathered}$$

The points on the graph are $\left(-\frac{\mathrm{Ï€}}{4},-1\right),(0,0),\left(\frac{\mathrm{Ï€}}{4},1\right)$.

The graph of the equation is: