Question

Plot the following two graphs on the same cartesian plain

Answer 1

The two functions are 1st degree polynomial, so they are both lines.

In order to draw a line, you have to sample two points and connect them.

To sample points from an equation, choose any value for x and compute the correspondent value for y.

For example, if we choose x=0 and x=1 for the first equation, we have

$f(x)=3x-2 \implies f(0)=-2,\quad f(1)=1$

So, the line passes through the points $(0,-2)$ and $(1,1)$

Similarly, if we choose x=0 and x=3 for the first equation, we have

$f^{-1}(x)=\dfrac{x}{3}+\dfrac{2}{3} \implies f(0)=\dfrac{2}{3},\quad f(3)=1$

So, this line passes through the points $\left(0,\frac{2}{3}\right)$ and $(3,1)$

If you draw the two points for each line and connect the pairs, you'll have the two lines.