Problem
Graph the following function. \[ h(x)=|-6 x| \] Determine the transformation(s) that need to be applied to $g(x)=|x|$ to obtain the graph of $h(x)=|-6 x|$ Select all that apply. A. Vertical stretch or shrink. B. Horizontal stretch or shrink. C. Reflect across $y$-axis. D. Reflect across $x$-axis. E. Vertical translation up. F. Vertical translation down. G. Horizontal translation to the left. H. Horizontal translation to the right.
Solution
Step 1 ：The function \(h(x)=|-6x|\) is a transformation of the function \(g(x)=|x|\).
Step 2 ：The transformation is a vertical stretch by a factor of 6 and a reflection across the y-axis.
Step 3 ：This is because the absolute value function \(|x|\) is being multiplied by -6, which stretches the graph vertically by a factor of 6 and reflects it across the y-axis.
Step 4 ：Final Answer: The correct transformations are \(\boxed{\text{A. Vertical stretch or shrink}}\) and \(\boxed{\text{C. Reflect across } y\text{-axis}}\).
