Question

can you answer this please...​

Answer 1

Given Question

Draw the graph of the function

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

$\green{\large\underline{\sf{Solution-}}}$

Given function is

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

Let assume that

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

Case :- 1

$\purple{\rm :\longmapsto\:When \: x > 0, \: \: y \: = \: 1}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 1 \\ \\ \sf 2 & \sf 1 \\ \\ \sf 3 & \sf 1 \end{array}} \\ \end{gathered}$

Case :- 2

$\purple{\rm :\longmapsto\:When \: x < 0, \: \: y \: = \: - \: 1}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf - 1 & \sf - 1 \\ \\ \sf - 2 & \sf - 1 \\ \\ \sf - 3 & \sf - 1 \end{array}} \\ \end{gathered}$

Case :- 3

$\purple{\rm :\longmapsto\:When \: x = 0, \: \: y \: = \: 0}$

So, Range of the function

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

$\purple{\rm :\longmapsto\:Range \: of \: f(x) \: = \: \{ - 1, \: 0, \: 1 \}}$

Answer 2

Given Question

Draw the graph of the function

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

$\green{\large\underline{\sf{Solution-}}}$

Given function is

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

Let assume that

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

Case :- 1

$\purple{\rm :\longmapsto\:When \: x > 0, \: \: y \: = \: 1}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 1 \\ \\ \sf 2 & \sf 1 \\ \\ \sf 3 & \sf 1 \end{array}} \\ \end{gathered}$

Case :- 2

$\purple{\rm :\longmapsto\:When \: x < 0, \: \: y \: = \: - \: 1}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf - 1 & \sf - 1 \\ \\ \sf - 2 & \sf - 1 \\ \\ \sf - 3 & \sf - 1 \end{array}} \\ \end{gathered}$

Case :- 3

$\purple{\rm :\longmapsto\:When \: x = 0, \: \: y \: = \: 0}$

So, Range of the function

$\begin{gathered}\begin{gathered}\bf\: f(x) \: = \: \begin{cases} &\sf{ \: \: 1, \: \: if \: x > 0} \\ &\sf{ \: \: 0, \: \: if \: x = 0} \\ &\sf{ - 1 \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

$\purple{\rm :\longmapsto\:Range \: of \: f(x) \: = \: \{ - 1, \: 0, \: 1 \}}$