How do you graph # y=2+sin(1/2x)#?
1 Answer
Draw a sine wave with twice the wavelength. Then shift it UP two units.
Explanation:
You know what the graph of
- when
#x# is#0, y = 0# - when
#x# is#pi/2, y=1# - when
#x# is#pi, y=0# - when
#x# is#(3*pi)/2, y=-1# - when
#x# is#2*pi, y=0#
graph{sin(x) [-10, 10, -5, 5]}
So now, for
- when
#x# is#0, x/2# is#0 , y= 0# - when
#x# is#pi, x/2# is#pi/2, y= 1# - when
#x# is#2 * pi, x/2# is#pi , y= 0# - when
#x# is#3 * pi, x/2# is#(3*pi)/2 , y= -1# - when
#x# is#4 * pi, x/2# is#2 * pi , y= 0#
So, it's the same sine wave, but stretched out.
Now, since your function is
- when
#x# is#0, y= 2# - when
#x# is#pi, y= 3# - when
#x# is#2 * pi, y= 2# - when
#x# is#3 * pi, y= 1# - when
#x# is#4 * pi , y= 2#
graph{2 + sin(x/2) [-10, 10, -5, 5]}