Question

Plot the graph of linear equation says \[f(x) = |3x - 2|\]?

Answer 1

Hint:Mod sign means the function will open with two signs, that means when you remove the mod sign you will get a positive as well as negative sign with the function, if the function does not change with negative sign then no issue, but if function will change with negative sign then you have to solve two functions one with positive sign and other with negative sign.

Complete step by step solution:
The given function is \[f(x) = |3x - 2|\]
Here after removing mod sign we get new functions as:
\[ \Rightarrow f(x) = |3x - 2| = \pm (3x - 2)\]
Now we have obtained two equations for which the graph needed to be plotted, on solving for the coordinates of both the graph we get:
\[
\Rightarrow f(x) = |3x - 2| = \pm (3x - 2) \\
\Rightarrow f(x) = 3x - 2\,for\,x = 0and1 \\
\Rightarrow f(x) = 3(0) - 2,3(1) - 2 = - 2,\, - 1 \\
\Rightarrow f(x) = - (3x - 2) = - 3x + 2,\,for\,x = 0and1 \\
\Rightarrow f(x) = - 3(0) + 2, - 3(1) + 2 = 2,\, - 1 \\
{\text{coordinates}}\,{\text{for}}\,{\text{first}}\,{\text{equation}}\,(0, - 2),(1, - 1) \\
{\text{coordinates}}\,{\text{for}}\,{\text{second}}\,{\text{equation(0,2),(1, - 1)}} \\
\]
Here we get the coordinates for both the equation and now we can draw the plot for the equations between the “f(x)” and “x” axis, on plotting we get:

Additional Information: You have to be careful while finding the coordinates, it is a simple step just assume any real value of any one coordinate and with the help of a given equation find the value of another coordinate, when you get both the coordinates it's over.

Note: In linear graphs you have to find any two coordinates of the respective axis. . In such a question the assumption of one coordinate is up to you so it's recommended to always take a point as \[0\]. You can also satisfy these points in the equation to check if the points are correct or not.