Question

Complete the table for the function $g\left(x\right)=\left|2x+3\right|$at $x=-3,-2,0,1,3$.

Short answer

The complete table of the given function is:

$x$	-3	-2	0	1	3
$g\left(x\right)$	3	1	3	5	9

Step-by-step solution

Step 1. Evaluate gx at x=−3,−2,0.

From the given function,

$g\left(x\right)=|2x+3|\mathrm{....}\left(1\right)$

Evaluate the value of function at$x=-3,-2,0$ gives,

role="math" localid="1644490769460" $$\begin{gathered} g\left(-3\right)=|2\left(-3\right)+3|\mathrm{....}\left(\text{Substitute}x=-3\text{in}\left(1\right)\right) \\ =|-3| \\ =3 \\ g\left(-2\right)=|2\left(-2\right)+3|\mathrm{....}\left(\text{Substitute}x=-2\text{\hspace{0.17em}in}\left(1\right)\right) \\ =|-1| \\ =1 \\ g\left(0\right)=|2\left(0\right)+3|\mathrm{....}\left(\text{Substitute}x=0\text{\hspace{0.17em}in}\left(1\right)\right) \\ =\left|3\right| \\ =3 \end{gathered}$$

Step 2. Evaluate gx at x=1,3.

Similarly, evaluate the value of function at $x=1,3$gives,

role="math" localid="1644490968973" $$\begin{gathered} g\left(1\right)=|2\left(1\right)+3|\mathrm{....}\left(\text{Substitute}x=1\text{in}\left(1\right)\right) \\ =\left|5\right| \\ =5 \\ g\left(3\right)=|2\left(3\right)+3|\mathrm{....}\left(\text{Substitute}x=3\text{\hspace{0.17em}in}\left(1\right)\right) \\ =\left|9\right| \\ =9 \end{gathered}$$

Step 3. Description of steps.

From the obtained values the required table is shown below.

$x$	-3	-2	0	1	3
role="math" localid="1644491067594" $f\left(x\right)$	3	1	3	5	9