how does multiplying x in an absolute value function alter the graph?

Question

I'm trying to solve the question "Plot y= |-4x|+3 and y= -4|x|+3 on the same set of axes." but I don't know what multiplying x by -4 does to the graph.

 

Answer 1

Plot y= |-4x|+3 and y= -4|x|+3.

 

The first graph has its lowest point when x = 0, when y = 3. 

From (0,3) the graph moves upward, with slope 4, as x increases.

From (0,3) the graph moves upward, with slope -4, as x decreases. The overall shape is a V.

 

The second graph has its highest point at (0,3). Going to either side of that peak, the graph has an upside-down V shape.

 

Verify this by plotting # 1 in blue and # 2 in red, using a table of values for x = -3 up through x = 3.