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

Question

Savannah Anderson · Accepted Answer

Use the graph of the parent function #f(x)=absx# but change the slope to of each half of the graph to #+-2#, and shift the vertex right one unit and down three units.

The parent function of absolute value is #f(x)=abs(x)# and looks like the graph below. Note the vertex is at #(0,0)# and the slope of the left branch of the graph is #-1# while the slope of the right branch is #+1#. graph{abs(x) [-10, 10, -5, 5]} Given the form, #f(x)=mabs(x-h)+k#, #+-m# represents the slope of each branch of the graph. A positive value of #m# in the original equation means the graph has a "V" shape, while a negative value of #m# means the graph has an "upside-down V-shape". #(h,k)# is the vertex. The vertex is shifted horizontally by h units and vertically by k units. #f(x)=2abs(x-1)-3# In this example, #m=2# is positive, and the graph will have a V-shape. The left branch of the V has a slope of #-2# and the right branch has a slope of #2#. The vertex is #(1,-3)#, which represents a shift of one unit to the right and 3 units down. graph{2abs(x-1)-3 [-10, 10, -5, 5]}

Nathan Axel · Answer

undefined To graph the function f(x) = 2|x-1| - 3, follow these steps:
1. Identify key points:
   - The vertex is at (1, -3).
   - The slope on the right side of the vertex is 2, and on the left side, it's -2.
2. Plot the vertex at (1, -3).
3. From the vertex, use the slope to plot additional points on both sides of the vertex.
4. Draw straight lines connecting these points, making sure to maintain the slope on each side.
5. The graph should resemble a "V" shape, with the vertex at the bottom.
6. Label the axes and any other relevant points or features on the graph.