Question

The function f(x)=16sinx contains which type of transformation or change to its parent graph? phase shift, vertical shift, horizontal stretch or change in period, vertical stretch or change in amplitude

Answer 1

The parent graph would be f(x) = sin(x).

The 16 coefficient represents a vertical stretch because the y-values of the graph expand out further. That is, on the parent graph, f(pi/2) = 1 while on the the function 16sin(x), f(pi/2) = 16. As you can see the graph is stretched out vertically.

Answer 2

Answer :

Option D is true.

Explanation:

We are given that a function f(x)=16 sin x

We have to find out which type of transformation or change to its parent graph.

We have parent function f(x)=sin x

Given function, f(x)= 16 sin x

If we are substituting
`x=(\pi)/(2)`

Then value of parent function
`f((\pi)/(2))= sin(\pi)/(2)=1`

because
`sin (\pi)/(2)=1`

The value of given function
`f(x)= 16 sin(\pi)/(2)`=16

Hence, the value of given function is 16 times the value of parent function.

Therefore, the given function contains vertical stretch or change in amplitude .

Option D is true.