Question

question 9 (mandatory) (1 point)
the point (2, 6) is on the graph of ( y = f(x) ). what are the coordinates of the image of this point on the graph ( y = f(4x) )?
a) (8, 24)
b) ( left( \frac { 1 } { 2 }, 6
ight) )
c) ( left( \frac { 1 } { 2 }, \frac { 3 } { 2 }
ight) )
d) (8, 6)

Explanation:

Step1: Analyze the transformation of the function

For the function \(y = f(4x)\), it is a horizontal compression of the function \(y = f(x)\) by a factor of \(\frac{1}{4}\).
When \(y = f(x)\) has a point \((x,y)\), for \(y = f(4x)\), we set \(4x_{new}=x_{old}\).
Given \(x_{old} = 2\), then \(4x_{new}=2\).

Step2: Solve for \(x_{new}\)

From \(4x_{new}=2\), we can solve for \(x_{new}\) by dividing both sides of the equation by \(4\). So \(x_{new}=\frac{2}{4}=\frac{1}{2}\).
The \(y -\)value remains the same in a horizontal - compression transformation (because the transformation is only along the \(x -\)axis), so \(y_{new}=y_{old} = 6\).

Answer:

B. \((\frac{1}{2},6)\)