Use transformations of the absolute value function, f(x)=|x|, to graph the function g(x)=-4|x+6|-5.
What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)?
Answer
\(\boxed{\text{The transformations needed to obtain the graph of } g(x) \text{ from the graph of } f(x) \text{ are a horizontal shift of 6 units to the left, a vertical shift of 5 units down, a vertical stretch by a factor of 4, and a reflection over the x-axis.}}\)
Step 1 ：The function g(x)=-4|x+6|-5 is a transformation of the absolute value function f(x)=|x|.
Step 2 ：The transformations needed are a horizontal shift of 6 units to the left, indicated by the '+6' inside the absolute value function.
Step 3 ：The function is also shifted 5 units down, indicated by the '-5' outside the absolute value function.
Step 4 ：The function is stretched by a factor of 4, indicated by the '-4' outside the absolute value function.
Step 5 ：Finally, the function is reflected over the x-axis, indicated by the negative sign outside the absolute value function.
Step 6 ：\(\boxed{\text{The transformations needed to obtain the graph of } g(x) \text{ from the graph of } f(x) \text{ are a horizontal shift of 6 units to the left, a vertical shift of 5 units down, a vertical stretch by a factor of 4, and a reflection over the x-axis.}}\)
