Question

fill in each blank so that the resulting statement is true.
the graph of ( y = f(6x) ) is obtained by a ____ shrink of the graph of ( y = f(x) ) by dividing each of its ____-coordinates by 6.
the graph of ( y = f(6x) ) is obtained by a horizontal shrink of the graph of ( y = f(x) ) by dividing each of its dropdown with x, y -coordinates by 6.

Explanation:

For function transformations, when we have \(y = f(kx)\) where \(k>1\), it creates a horizontal shrink. This transformation modifies the input (x-values) of the original function \(y=f(x)\), so we divide each x-coordinate by \(k\) (here \(k=6\)) to get the transformed graph.

Answer:

The graph of \(y = f(6x)\) is obtained by a horizontal shrink of the graph of \(y = f(x)\) by dividing each of its x-coordinates by 6.