Question

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
f(x)= cos x/4
g(x)= cos x

Answer 1

if you have

cos(bx) then the period is

\[\frac{2\pi}{b}\]

in the 1st curve f(x) it takes a distance of

\[\frac{2\pi}{1}\]

to complete 1 full cycle of the curve, this is known as the period.

in g(x) the value of b is 1/4

so the period is

\[\frac{2\pi}{\frac{1}{4}} = 8\pi\]

or the cycle of g(x) is 4 times longer than the cycle for g(x)

to change f(x) to g(x) the value of b, in f(x) is divided by 4

hope this makes sense.

Answer 2

\(\large {\textit{parent function } cos(x)\qquad
\begin{array}{cccllll}
g(x)=&cos\left(\frac{x}{\color{red}{4}}\right)\\
&\qquad \uparrow\\

\end{array}\\ \quad \\
\bf \textit{period change from regular period of }2\pi\\ \quad \\
\textit{to new period of }\cfrac{2\pi}{\color{red}{4}}}\)

Answer 3

is it a horizontal or vertical shift of 1/4

Answer 4

there is no shift..... the curve g(x) is stretched by a factor of 4

have a look at the graphs

g(x) takes a distance of 8pi to complete a cycle... and f(x) takes a distance of 2pi

or f(x) completes 4 cycles over the same distance it takes g(x) to complete 1 cycle