Question

Which graph represents the function r(x) = |x-2| -1

Answer 1

It's whichever graph is an absolute function and is shifted to the right by 2 and is shifted down by 1.

Since I don't have a picture of the graph this is the best I can do to help.

Answer 2

Answer:

see attached

Step-by-step explanation:

Translations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

Given function:

$r(x) = |x - 2| - 1$

The parent function of the given function is:  $f(x) = |x|$

Translated 2 units to the right:  $f(x-2)=|x-2|$

Translated 1 unit down:  $f(x-2)-1=|x-2|-1$

Graph of Modulus function

Line y = x where x ≥ 0

Line y = -x where x ≤ 0

Vertex at (0, 0)

Therefore, the graph of the given function is the graph of the modulus function translated 2 units to the right and 1 unit down.  So, its vertex is at (2, -1).

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