Question

Write the equation of the graph which is the reflection of y=−|x−1|−1 about the origin

Answer 1

The equation of the graph that represents the reflection of
`\(y = -|x - 1| - 1\)` about the origin is
`\(y = |x + 1| - 1\).`

Step-by-step explanation:

To find the equation of the graph that represents the reflection of
`\(y = -|x - 1| - 1\)` about the origin, we'll determine how the graph of the function
`\(y = -|x - 1| - 1\)`changes due to the reflection across the origin.

The graph
`\(y = -|x - 1| - 1\)`is a reflection of the absolute value function
`\(y = |x|\)` over the x-axis, shifted one unit to the right and down by one unit. When reflecting a graph about the origin, both the x and y values change signs.

For the original equation
`\(y = -|x - 1| - 1\),`to reflect it across the origin, the negative sign before the absolute value is reversed to a positive sign. Hence,
`\(y = |x + 1| - 1\)` represents the reflected graph.

The transformation from
`\(y = -|x - 1| - 1\) to \(y = |x + 1| - 1\)`involves replacing
`\(x\) with \(-x\)` to reflect the graph over the y-axis and changing the constant term from
`\(-1\) to \(1\)` to reflect it over the x-axis. This results in the equation
`\(y = |x + 1| - 1\)`, representing the graph of the function reflected about the origin.

Answer 2

f(x) = |x + 1| + 1

Step-by-step explanation:

A reflection over the y-axis followed by a reflection over x-axis is equivalent to a reflection about origin.

f(x) = -|x-1| -1

reflection over the x-axis:

-f(x) = (-1)*(-|x-1| -1) = |x-1| +1

reflection over the y-axis of the previous function:

-f(-x) = |-x-1| +1 = |x + 1| + 1

which is the reflection of f(x) about the origin