Question

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

Explanation:

Step1: Recall horizontal shrink rule

For a function \(y = f(x)\), if we have \(y=f(kx)\) where \(k> 1\), the graph of \(y = f(kx)\) is a horizontal shrink of the graph of \(y = f(x)\).

Step2: Analyze the transformation

For the function \(y = f(6x)\) (where \(k = 6\)), the transformation is a horizontal shrink. When we go from \(y=f(x)\) to \(y = f(6x)\), if \((x_1,y_1)\) is a point on \(y = f(x)\) (i.e., \(y_1=f(x_1)\)), then for \(y=f(6x)\), when \(y = y_1\), \(x=\frac{x_1}{6}\). So we divide the \(x -\)coordinates of the points on \(y = f(x)\) by \(6\) to get the points on \(y=f(6x)\).

Answer:

horizontal; \(x-\)