Question

What is the graph of the function rule?
y=I4xI+3
Which way will the lines point up or down

Answer 1

\[y-3=\left| 4x \right|\]
\[y-3=4x ,if x \ge 0 ,i.e.,y-3\ge 0 or y \ge 3\]
\[y-3=-4x ,if x <0 or R.H.S. is positive.\]
\[y-3 \ge 0 or y \ge 3\]
\[In either case y \ge 0\]
so you see lines are upward.

Answer 2

Here's a way of thinking about it.
The absolute value of 4x tells you no matter what x value you put in, positive or negative, |4x| will always be greater than 0.
Obviously the +3 is greater than 0 as well.
So the graph is pointing upwards.

Answer 3

would the lines go up from 3 or -3 @surjithayer

Answer 4

from3

Answer 5

How the graph would look.

y=4x would just be a straight line going from bottom left to top right.
y=|4x| would be the same, except when the x values become negative you get positive values mirroring the other side.
So the line would bend at the origin and you would get two lines that reflect each other.

y=x+3 has the effect of shifting the entire graph of y=x up by 3 points. So in y=|4x|+3 it would shift the graph of y=|4x| up by 3 points.