Chapter 7, Problem 1RVS

To determine

The correct graph of the function $f\left(x\right)=x$ from the provided options.

Answer to Problem 1RVS

Solution:

The correct graph of the function $f\left(x\right)=x$ is D and the graph is as follows,

Explanation of Solution

Given information:

The function is given as $f\left(x\right)=x$ and

The options given for graph are as follows,

Consider the providedfunction,

$f\left(x\right)=x$

To identify the graph, it must be necessary to know about minimum three co-ordinates,

To find the co-ordinate of the graph just substitute the value of $x$ corresponding to this we get the values of $y$,

Now, rewrite the function as,

$y=f\left(x\right)=x$

Substitute the value of $x=1$ in the equation $y=x$,

$\begin{array}{l}y=x\\ y=1\end{array}$

So, the first co-ordinate of the function is $\left(1,1\right)$.

Substitute the value of $x=-1$ in the equation $y=x$,

$\begin{array}{l}y=x\\ y=-1\end{array}$

So, the second co-ordinate of the function is $\left(-1,-1\right)$.

Substitute the value of $x=0$ in the function $y=x$,

$\begin{array}{l}y=x\\ y=0\end{array}$

So, the third co-ordinate of the function is $\left(0,0\right)$.

The co-ordinates $\left(1,1\right),\left(-1,-1\right)\text{ and }\left(0,0\right)$ matches with the co-ordinates of the graph from the options and option is D.

Therefore, the correct graph of the function $f\left(x\right)=x$ is D.