How do I graph f(x)=2|x-4|+6?

Question

All the problem says is to graph it

Answer 1

y=2*abs(x-4)+6

yu hav a big V...2 strate lines, bottom at y=2*6=12...point=(4,12)

slope=+2 on rite side (x> 4)...angel=invers tan(2)=63.43494882292 deg

left side up 63.43 deg from -180deg...-116.565051177 deg

Answer 2

Given: f(x)=2lx-4l+6   First,draw a graph of f(x)=2lxl

1. On the interval x≥0: The graph is a ray that goes up rightwards at slope of 2:1.

2. On the interval x<0: The graph is the mirror of right-hand ray reflected about the y-axis.   You now have a graph: f(x)=lxl.   The slope of the left^hand ray is -2:1, The 2 rays opens upwards forming a letter-V vertex at the bottom: the origine of coordinate plane,O(0,0). 

3. f(x)=2lx-4l is f(x)=lxl moved 4 units to the right.   You dont need to draw the new graph, but just change the coordinates of vertex(0,0) to (4,0).   You now have a new graph: f(x)=2lx-4l

4. f(x)=2lx-4l+6 is f(x)=2lx-4l moved 6 units upwards.   Change the coordinates of vertex(4,0) to(4,6).   Draw a new x-axis 4 units left fome the original, and a new y-axis 6 units downwards.

You now have the graph: f(x)=2lx-4l+6