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.
Answer
Final Answer: The correct transformations are \(\boxed{\text{A. Vertical stretch or shrink}}\) and \(\boxed{\text{C. Reflect across } y\text{-axis}}\).
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 \(\boxed{\text{C. Reflect across } y\text{-axis}}\).
