Chapter 12, Problem 1RVS

To determine

The graph of the function $f\left(x\right)=2x-3$ from the given graphs.

A.

B.

C.

D.

E.

F.

G.

H.

I.

J.

Answer to Problem 1RVS

Solution:

The graph of the function $f\left(x\right)=2x-3$ matches with the graph of “J”.

Explanation of Solution

Given Information:

The Function is $f\left(x\right)=2x-3$.

Consider the function:

$f\left(x\right)=2x-3$

Assume,

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

Then,

$y=2x-3$

Substitute $x=0$ in equation $y=2x-3$ to calculate the y-intercept.

$\begin{array}{c}y=2\left(0\right)-3\\ =0-3\\ =-3\end{array}$

Substitute $y=0$ to calculate the x-intercept.

$\begin{array}{c}0=2x-3\\ 2x=3\\ x=\frac{3}{2}\end{array}$

Substitute $x=2$ in the equation $y=2x-3$ to calculate a third point.

$\begin{array}{c}y=2\left(2\right)-3\\ =4-3\\ =1\end{array}$

Make the table to write the obtained values of $x$ and $y$, thus the ordered pairs.

$\begin{array}{lll}x\hfill & y\hfill & \left(x,y\right)\hfill \\ 0\hfill & -3\hfill & \left(0,-3\right)\hfill \\ \frac{3}{2}\hfill & 0\hfill & \left(\frac{3}{2},0\right)\hfill \\ 2\hfill & 1\hfill & \left(2,1\right)\hfill \end{array}$

Now, draw the graph:

Thus, the function $f\left(x\right)=2x-3$ matches with the graph of “J”.