Chapter 10, Problem 1RVS

To determine

The graph for the function $f\left(x\right)=2x-5$ and match the correct graph from the provided set of options.

Answer to Problem 1RVS

Solution:

The correct match for the function is the graph in the option B.

Explanation of Solution

Given Information:

The provided function is $f\left(x\right)=2x-5$.

The set of options for correct solution is,

A.

B.

C.

D.

E.

F.

G.

H.

I.

J.

Consider the provided function is,

$f\left(x\right)=2x-5$

Determine the values of the function $f\left(x\right)=2x-5$ for some random values of x as,

Substitute $x=0$ in the function $f\left(x\right)=2x-5$.

$\begin{array}{ccc}\hfill f\left(x\right)& =& 2\cdot 0-5\hfill \\ \hfill & =& -5\hfill \end{array}$

Substitute $x=1$ in the function $f\left(x\right)=2x-5$.

$\begin{array}{ccc}\hfill f\left(x\right)& =& 2\cdot 1-5\hfill \\ \hfill & =& -3\hfill \end{array}$

Substitute $x=-1$ in the function $f\left(x\right)=2x-5$.

$\begin{array}{ccc}\hfill f\left(x\right)& =& 2\cdot -1-5\hfill \\ \hfill & =& -7\hfill \end{array}$

Substitute $x=2$ in the function $f\left(x\right)=2x-5$.

$\begin{array}{ccc}\hfill f\left(x\right)& =& 2\cdot 2-5\hfill \\ \hfill & =& -1\hfill \end{array}$

Substitute $x=-2$ in the function $f\left(x\right)=2x-5$.

$\begin{array}{ccc}\hfill f\left(x\right)& =& 2\cdot -2-5\hfill \\ \hfill & =& -9\hfill \end{array}$

Now, the form the table for the value of x and $f\left(x\right)$ which is shown below,

$\begin{array}{cc}x& f\left(x\right)=2x-5\\ 0& -5\\ 1& -3\\ -1& -7\\ 2& -1\\ -2& -9\end{array}$

Thus, coordinates are $\left(0,-5\right),\left(1,-3\right),\left(-1,-7\right),\left(2,-1\right),\left(-2,-9\right)$.

The graph of the function $f\left(x\right)=2x-5$ is shown below,

Hence, graph in option B is the correct graph.

Let’s check for each graph as,

Graph in option A is a line graph that passes through origin but obtained coordinates have different value at $x=0$, so it is not the correct graph.

Graph in option B is a line graph that cuts the y-axis at $\left(0,-5\right)$ that matches the obtained coordinates. Also, all other coordinates match the line graph.

Graph in option C is a curve that passes through origin but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option D is a line graph that passes through origin but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option E is a line graph that that cuts the y-axis at $\left(0,4\right)$ but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option F is a line graph that that cuts the y- axis at $\left(0,4\right)$ and x-axis at $\left(4,0\right)$ but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option G is a line graph parallel to y-axis that that cuts the y-axis at $\left(0,-2\right)$ but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option H is an upward parabola with vertex at $\left(0,-1\right)$ cuts the x-axis at $\left(-1,0\right)$ and $\left(1,0\right)$ but equation is of line graph and obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option I is a line graph that that cuts the y-axis at $\left(0,-2\right)$ and x-axis at $\left(2,0\right)$ but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Graph in option J has two straight lines in different directions where one line cuts the -axis at $\left(0,5\right)$ and both meet at point $\left(2.5,0\right)$ but obtained coordinates are different and have different value at $x=0$, so it is not the correct graph.

Therefore, the correct match for the function is the graph in the option B.