graph y=sin2x, and y=sin1/2x . How does the k value affect the graphs? Describe the transformation in words. What key feature of the graph is changed?

Answer 1

I suggest you go to Wolfram and graph the following:
y = sinx
y = sin(2x)
y = sin(3x)
y = sin(1/2x)
y = (1/4x)
etc

keep the y = sinx with each case, as a reference
e.g.
https://www.wolframalpha.com/input/?i=graph+y+%3D+sinx%2C+y+%3D+sin%282x%29

Answer 2

new link
https://www.wolframalpha.com/input/?i=graph+y+%3D+sinx%2C+y+%3D+sin%282x%29%2C+0+%3C+x+%3C+2%CF%80

I wanted the domain from 0 to 2π
and I wanted you to compare the number of complete cycles of the sine curve
for y = sin kx , from 0 to 2π

Answer 3

sin(kx) has a period of 2π/k