Step 1
Given;
Step 2
Find the equation of f(x)
[tex]\begin{gathered} y=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1} \\ y_2=0 \\ y_1=-2 \\ x_2=2 \\ x_1=1 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{0-(-2)}{2-1}=\frac{2}{1}=2 \\ y=0,x=2 \\ 0=2(2)+b \\ b=-4 \end{gathered}[/tex][tex]f(x)=2x-4[/tex]
Thus g(x) will be;
[tex]g(x)=\frac{1}{2}((2x+3)-4)[/tex][tex]\begin{gathered} g(x)=\frac{1}{2}(2x-1) \\ g(x)=x-\frac{1}{2} \end{gathered}[/tex]
Thus the points of g(x) will be;
[tex]\begin{gathered} g(0)=-\frac{1}{2} \\ g(1)=\frac{1}{2} \\ g(2)=\frac{3}{2} \\ g(3)=\frac{5}{2} \\ g(4)=\frac{7}{2} \end{gathered}[/tex]
The graph will be;
