Question

the graph of a function f was translated 4 units right. the translated graph is shown. write an equation for f(x)

Answer 1

The transformed function is
`\( g(x) = |2x| - 4 \),` obtained by shifting the original function
`\(4\)` units downward.

The given function is
`\( f(x) = |2x| \)`. To translate this function 4 units down, we need to subtract 4 from the entire function. The vertical translation of a function
`\( f(x) \)` downwards by
`\( k \)` units is represented as
`\( f(x) - k \)`.

Therefore, the transformed function
`\( g(x) \)` is obtained by subtracting 4 from
`\( g(x) \)`
`\( f(x) \):`

`\[ g(x) = |2x| - 4 \]`

This transformation shifts every point on the graph of
`\( f(x) = |2x| \)`downward by 4 units. The absolute value function
`\( |2x| \)`is symmetric about the y-axis, so the translation affects both the positive and negative regions of the x-axis equally.

In summary, the equation of the transformed function is
`\( g(x) = |2x| - 4 \),` indicating a vertical translation downward by 4 units compared to the original function
`\( f(x) = |2x| \).` The absolute value function ensures that the graph remains V-shaped, but it is now positioned lower on the coordinate plane.

Question:

The graph of the function f(x)=|2x| is translated 4 units down. What is the equation of the transformed function?