Chapter 1, Problem 4CT

To determine

To sketch: The graph for the equation.

Answer to Problem 4CT

The sketch for the graph of equation $y=4-\left|x\right|$ is shown in Figure 1

Explanation of Solution

Given:

The given equation is $y=4-\left|x\right|$ .

Calculation:

Consider the given equation,

  $y=4-\left|x\right|$ ..............(I)

Consider the value of $x=1$ . Then the equation is,

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

Consider the value of $x=-1$ . Then the equation is,

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

The value of y of the equation $y=4-\left|x\right|$ is symmetricto both the axis.

Consider the value of $y=1$ . Then the equation is,

  $\begin{array}{c}1=4-\left|x\right|\\ x=\pm 3\end{array}$

Consider the value of $y=-1$ . Then the equation is,

  $\begin{array}{l}-1=4-\left|x\right|\\ x=\pm 5\end{array}$

The value of x is different for both the x axis thus the equation $y=4-\left|x\right|$ is not symmetric to both the axis.

To determine the value of the y intercept substitute $0$ for $x$ in the equation (I).

  $\begin{array}{c}y=4-\left|0\right|\\ =4\end{array}$

To determine the value of the y intercept substitute $0$ for $y$ in the equation (I).

  $\begin{array}{c}0=4-\left|x\right|\\ x=\pm 4\end{array}$

The value of $y$ intercept of the equation is $\left(4,0\right)$ and the value of the x intercept are $\left(4,0\right)$ and $\left(-4,0\right)$ .

Mark the intercepts and draw the graph for the equation.

The required diagram is shown in Figure 1

  

Figure 1