Write the function whose graph is the graph of y=l x l but is shifted up 9 units.

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k

∵ y = IxI

∵ The graph of the function is shifted 9 units up

- That means the graph of the function is translated 9 units, up

∵ The equation of the function f(x) whose graph shifted k units

up is f(x) + k

∵ k = 9

∴ The equation of the function is y = IxI + 9

The function is y = IxI + 9

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xero099 xero099 · Answer 2 · 2021-11-23T13:46:52+01:00

The translated function is [tex]g(x) = |x|+9[/tex].

Mathematically speaking, a vertical translation is defined by the following operation:

[tex]g(x) = f(x) + k[/tex] (1)

Where:

The original function is shifted up when [tex]k > 0[/tex].

If we know that [tex]f(x) = |x|[/tex] and [tex]k = 9[/tex], then the translated function is [tex]g(x) = |x|+9[/tex].

We kindly invite to check this question on translations: https://brainly.com/question/12463306