Question

Graph the function f x x ( ) 1 2 .

Answer 1

From the problem, we have the function :

`f(x)=\lvert x+1\rvert+2`

Note that an absolute value function is in V-shape and the vertex will be (h, k) :

`f(x)=\lvert x-h\rvert+k`

The vertex is at (-1, 2) and we need another two points to graph this function.

`\begin{gathered} \text{when x = }2 \\ f(2)=|2+1|+2 \\ f(2)=3+2=5_{} \\ \\ \text{when x = -}4 \\ f(-4)=|-4+1|+2 \\ f(-4)=3+2=5 \end{gathered}`

The points are (2, 5) and (-4, 5) with a vertex at (-1, 2).

Plot the points into the rectangular coordinate system.

The graph will be :