Question

The absolute value parent function f (x) = x is reflected across the x-axis, horizontally translated left 5 units, and

vertically translated up 9 units. Determine of the new function will have a local maximum or minimum and its value.

Answer 1

The new function will not have a local maximum or minimum. Its value will be shifted vertically up by 9 units.

Step-by-step explanation:

To determine if the new function will have a local maximum or minimum and its value, we need to analyze the transformations applied to the parent function f(x) = x. The function was reflected across the x-axis, horizontally translated left 5 units, and vertically translated up 9 units.

When the function is reflected across the x-axis, the sign of the function changes, but it does not affect whether it has a local maximum or minimum. The horizontal translation to the left does not affect the local maximum or minimum either. The vertical translation up 9 units does not affect the local maximum or minimum, but it shifts the entire graph upwards.

Since the parent function f(x) = x does not have a local maximum or minimum, the new function after the transformations will also not have a local maximum or minimum. Its value will be shifted vertically up by 9 units compared to the parent function.