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Which absolute value function corresponds to the graph with these characteristics?
. The vertex is at (2,4).
• As x approaches negative infinity, f(x) approaches positive infinity.
• The domain is all real numbers.
. It is decreasing on the interval (-∞, 2).
OA.
x)= |x-21-4
O B.
f(x)= |x-21 +4
OC.
fx)= x+21 +4
O D. f(x)= |x+21-4

Respuesta :

Using translation concepts, the absolute value function with these characteristics is given by:

f(x) = |x - 2| + 4.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent absolute value function is given by:

f(x) = |x|

And has vertex at (0,0).

With the vertex at (2,4), we have that:

  • The function was shifted 2 units right, hence x -> x - 2.
  • The function was shifted 4 units up, hence f(x) - > f(x) + 4.

Hence the absolute value function with these characteristics is given by:

f(x) = |x - 2| + 4.

More can be learned about translation concepts at https://brainly.com/question/4521517

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