contestada

What is the range of the function f(x) = |x + 4| + 2?

R: {f(x) ∈ ℝ | f(x) ≤ 2}
R: {f(x) ∈ ℝ | f(x) ≥ 2}
R: {f(x) ∈ ℝ | f(x) > 6}
R: {f(x) ∈ ℝ | f(x) < 6}

Respuesta :

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Given:

▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]

You need to remember that the form of an Absolute Value Function is:

• For the vertex:

[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]

[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]

• For the definition:

If "a" is positive (+) , then the range of the function is:

[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]

If "a" is negative (-), the range of the function is:

[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]

In this case we can identify that:

[tex]\small\longrightarrow \sf{a = 1}[/tex]

[tex] \small\longrightarrow\sf{a = 2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]

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