Chapter 9.9, Problem 61S

To determine

Graph the function $g\left(x\right)=\left|3x+4\right|$ .

Answer to Problem 61S

  

Explanation of Solution

Given:

The function: $f\left(x\right)=\left|x-2\right|$

Concept Used:

The  x -intercepts are where the graph crosses the  x -axis, and the  y -intercepts are where the graph crosses the  y -axis.

Then, algebraically,

• an  x -intercept is a point on the graph where  y  is zero, and
• a  y -intercept is a point on the graph where  x  is zero.

More specifically,

• an  x -intercept is a point in the equation where the  y -value is zero, and
• a  y -intercept is a point in the equation where the  x -value is zero.

Calculation:

The function: $g\left(x\right)=\left|3x+4\right|$

We can graph the function by using x and y − intercept method. First we find the x and y intercept from the equation and then plot the points on the grid and join then to complete the graph.

Find the x − intercept, plug in y = 0 in the equation.

  $\begin{array}{c}g\left(x\right)=\left|3x+4\right|\\ 3x+4=0[\text{Plug}\text{in}y=0]\\ 3x+4-4=-4\\ 3x=-4\\ \frac{3x}{3}=\frac{-4}{3}\\ g\left(x\right)=-1.33\end{array}$ x − Intercept: $x=-1.33$

Find the y − intercept, plug in x = 0 in the equation $\begin{array}{c}g\left(x\right)=\left|3x+4\right|\\ g\left(x\right)=3x+4[\text{Plug}\text{in}x=0]\\ =3\times 0+4\\ g\left(x\right)=4\end{array}$ y − Intercept: $y=4$

Graph the line $g\left(x\right)=\left|3x+4\right|$ with x and y intercepts points are (-1.33, 0) and (0, 4)

  

Thus, x and y intercepts are x = -10 and y = 5 .