Question

Graph g(x) = 5.2 – 6 + 2.y65+43+21-7 -6 -5 4 3 2112 3 4 56 7-2--3+-4-5+-6+7

Answer 1

we have the function

`g(x)=5\mleft|x-6\mright|+2`

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)

`\begin{gathered} g(10)=5|10-6|+2 \\ g(10)=5|4|+2 \\ g(10)=22 \end{gathered}`

we have the point (10,22)

For x=0 (at left of the vertex)

`\begin{gathered} g(0)=5|0-6|+2 \\ g(0)=5|-6|+2 \\ g(0)=32 \end{gathered}`

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