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Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range. (5 points) Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| − 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?



Answer :

The translation used on the graph is that its is shifted horizontally to the left by 3 units.

Translation is the procedure by which a graph is shifted from its original position to another position on the cartesian plane.

Now translation can be of three kinds:

  • Vertical or horizontal shift of the graph
  • Rotation around a fixed point
  • Dilation

The given function is of the form  g(x) = |x + 3| , the parent function is

[tex]f(x) = |x|[/tex] .

So from the graphs attached we can conclude that the translation that is used is horizontal shift by 3 units to the left.

Domain:  (−∞,∞),{x | x ∈ R}

Range:    [0,∞) , {y | y ≥ 0}

Vertex is at ( - 3 , 0 ).

The vertex of the parent function is at ( 0 , 0)  so the vertex of the translated function h(x) =|x|-2 is at  ( 0 , -2 ) .

The range of f(x) is {y| y ≥ 0 , y ∈ R}

The range of function h(x) :  [−2,∞),{y | y ≥ − 2}

To learn more about translation visit:

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