How do you graph #f(x)=2abs(x-1)-3#?

Question

Abigail Allen · Accepted Answer

Plot the point where #(x-1) = 0# and one point for each of #(x-1) > 0# and #(x-1) < 0#; connect the initial point through each of the other 2 points as 2 line segments.

Given #f(x) = 2abs(x-1) -3#

When #x= 1#
#color(white)("XXXX")##f(1) = -3#
#(1,-3)# is a point common to both line segments (#x<=1# and #x>=1#)

Picking #x=3# as an arbitrary point with #x > 1#
#color(white)("XXXX")##f(3) = 2abs(3-1) -3 = 1#
#(3,1)# is a point on the line segment for #x >1#

Picking #x=0# as an arbitrary point with #x < 1#
#color(white)("XXXX")##f(0) = 2abs(0-1) -3 =-1#
#(0,-1)# is a point on the line segment for #x < 1#

Hazel Anglin · Answer

undefined To graph the function $ f(x) = 2| x - 1 | - 3 $, follow these steps:

1. Identify the key points:
   - Vertex: The vertex occurs at the point (1, -3).
   - Slope: The slope of the absolute value function is 2.

2. Plot the vertex at (1, -3).

3. Use the slope to plot additional points:
   - From the vertex, move one unit to the right and two units up to plot the point (2, -1).
   - Move one unit to the left from the vertex and two units up to plot the point (0, -1).

4. Draw a V-shape connecting these points.

5. Label the axis and any other necessary information on the graph.