Question

Which absolute value function corresponds to the graph with these characteristics?

Answer 1

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 brainly.com/question/4521517

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