Question

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}qqR: {f(x) ∈ ℝ | f(x) < 6}

Answer 1

Given the Absolute Value Function:

$f(x)=|x+4|+2$

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

$y=a|x-h|+k$

Where "h" is the x-coordinate of the vertex, and "k" is the y-coordinate of the vertex. If "a" is positive the function opens up, and if it is negative, the function opens down.

By definition:

- If "a" is positive, then the Range of the function is:

$R:y\ge k$

- If "a" is negative, the Range of the function is:

$R:y\leq k$

In this case, you can identify that:

$\begin{gathered} a=1 \\ k=2 \end{gathered}$

Therefore, you can determine that its Range is:

$R:\lbrace f(x)\in R|f(x)\ge2\rbrace$

Hence, the answer is: Second option.