we have the function
[tex]g(x)=5\mleft|x-6\mright|+2[/tex]we know that
the vertex of this function is the point (6,2)
To graph a linear absolute value function, we need at least three points
the vertex , one point at right of the verrtex and one point at left of the vertex
so
For x=10 (right of the vertex)
substitute in g(X)
[tex]\begin{gathered} g(10)=5|10-6|+2 \\ g(10)=5|4|+2 \\ g(10)=22 \end{gathered}[/tex]we have the point (10,22)
For x=0 (at left of the vertex)
[tex]\begin{gathered} g(0)=5|0-6|+2 \\ g(0)=5|-6|+2 \\ g(0)=32 \end{gathered}[/tex]we have the point (0,32)
using a graphing tool
Plot the given points and join them to graph the function
see the attached figure
please wait a minute to plot the points
