Respuesta :

If you start from the "standard" sine function, i.e.

[tex] y = \sin(x) [/tex]

You can change its graph in four ways:

Amplitude: you can multiply the whole function by a constant to stretch/squeeze it vertically. The transformation looks like

[tex] y = \sin(x) \to y = k\sin(x) [/tex]

Phase: you can add a constant to the argument translate it horizontally. The transformation looks like

[tex] y = \sin(x) \to y = \sin(x+k) [/tex]

Period: you can multiply the argument by a constant to stretch/squeeze it horizontally. The transformation looks like

[tex] y = \sin(x) \to y = \sin(kx) [/tex]

Shift: you can add a constant to the whole function to translate it vertically. The transformation looks like

[tex] y = \sin(x) \to y = \sin(x)+k [/tex]

In your case, we're changing the period of the function. If [tex] k>1 [/tex] the function is squeezed, so you're squeezing the graph horizontally by a factor of 7/4