First equation
To graph the function, we make a table of values. We choose a few x-values and replace them into the equation to find the corresponding y-values of the ordered pairs through which the function passes.
Then, if we choose the values x = 1, x = 3, and x = 5, we have:
[tex]\begin{gathered} f(x)=-2x \\ f(1)=-2\cdot1 \\ f(1)=-2 \end{gathered}[/tex][tex]\begin{gathered} f(x)=-2x \\ f(3)=-2\cdot3 \\ f(3)=-6 \end{gathered}[/tex][tex]\begin{gathered} f(x)=-2x \\ f(5)=-2\cdot5 \\ f(5)=-10 \end{gathered}[/tex]
Now, we plot and join the above points:
Second function
We repeat the previous steps. If we choose the values x = 0, x = -2, and x = -3, we have:
[tex]\begin{gathered} g(x)=-2x-4 \\ g(0)=-2\cdot0-4 \\ g(0)=0-4 \\ g(0)=-4 \end{gathered}[/tex][tex]\begin{gathered} g(x)=-2x-4 \\ g(-2)=-2\cdot-2-4 \\ g(-2)=4-4 \\ g(-2)=0 \end{gathered}[/tex][tex]\begin{gathered} g(x)=-2x-4 \\ g(-3)=-2\cdot-3-4 \\ g(-3)=6-4 \\ g(-3)=2 \end{gathered}[/tex]
Now, we plot and join the above points:
Therefore, the graph of the given functions in the same rectangular coordinate system is:
