graph y=|3(x+2)|-1 and then show the tranformations axis of symmetry vertex and range and domain

Question

please help and solve the problem have no clue what there talking about with transformation

 

Answer 1

Star with the "v" of tge absolute value of x function described above.

 

Horizontally compress the function by a scale of 3, i.e. stretch each point horizontally about the y axis by a factor of 1/3. So (3,3) goes to (1,3), and (-3,3) goes to (-1,3).

 

Horizontally shift left by two units.

 

Vertically shift down by 1.

 

The x transformations are horizontal and are reversed both in order and in direction/scaling. The y transformations are direct.

Answer 2

Start with y = l x l.  The graph is "V shaped" with the point of the V at (0,0) and with axis of symmetry the y-axis.

 

Translate the graph 2 units to the left to get the graph of                    y = l x+2 l.

 

Horizontally compress the graph  of y = l x+2 l to obtain the graph of

y = l 3(x+2) l.

 

Vertically shift the graph of y = l 3(x+2) l down one unit to get the graph of y = l 3(x+2) l -1.

 

Axis of symmetry:  x = -2

Vertex:  (-2,-1)  (lowest point)

Domain:  (-∞, ∞) (set of all possible values of x)

Range: [-1, ∞) (set of all possible values of y)