Question

What is the domain and range of f(x)=2|x+2|-8

Answer 1

Answer:

The domain of f(x) is {x : x ∈ R} and the range is {y : y ≥ -8}

Step-by-step explanation:

- The domain of the function is the values of x which make the

  function defined

- The rang is the corresponding values of y with the domain

- The parent function of f(x) is g(x) = IxI

- The graph of this function represented by 2 lines starting from  

  the origin, one of them with positive slope and the other with negative

  slope and both of them over the x-axis

- The Domain of g(x) is {x : x ∈ R} where R is the set of real numbers

- That mean the domain of g(x) is all real numbers

- The range of g(x) is {y : y ≥ 0}

- That mean the range is all real numbers greater than or equal to zero

- f(x) is the image of g(x) after some transformations

- g(x) multiplied by 2 that mean vertical stretch.

- Then x add by 2 that mean horizontal translation to the left by 2 units

- Then subtract 8 from it means vertical translation down by 8 units

- The figure of f(x) is the same lines but stretched vertically away from

   x-axis and moved to the left 2 units and down 8 units

- That means the image of the origin is (-2 , -8)

- So the domain does not change it is the all real numbers

- The domain of f(x) is {x : x ∈ R}

- But the range changes is because the graph of the function starts

 from -8 not from 0

- Then the range of f(x) is {y : y ≥ -8}

* The domain of f(x) is {x : x ∈ R} and the range is {y : y ≥ -8}

- Look to the attached graph for more understand