What are the x and y intercept?

Question

What are the x and y intercepts of...

y=3sin(4x)

Answer 1

to find x and y intercepts you set either one to zero.

if its the y intercept (where the point is just on the y axis and x=0), set x = 0 so solve for y:

y=3sin(4*0)=3sin(0)=3*0=0

if its the x intercept (where the point is just on the x asix and y = 0), set y = 0 and solve for x:

0 = 3sin(4x)

divide by 3

0 = sin(4x)

Where is sin equal to zero? 0,pi,2pi etc. so,

4x = must equal 0, pi, 2pi or n(any integer)*pi

so x = n*pi/4

Answer 2

y intercept is 0, there is no horizontal shift of the graph

the x intercepts are at 0 +/- (pi)/4