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

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

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Answer 1 · 2014-09-27T15:30:31

Begin by finding out the range of $g (x) = | x + 4 |$ $g(x) = |x+4|$ , or for that matter, $g (x) = | x |$ $g(x) = |x|$ . The range is obviously given by $[0, \infty)$ $[0,\infty)$ for both of them.

Now, what is the range of $f (x) = | x + 4 | + 2$ $f(x) = |x+4| + 2$ ? It can be seen that the difference between $| x + 4 | + 2$ $|x+4| + 2$ and $| x + 4 |$ $|x+4|$ is $2$ $2$ . Literally.

If you add $2$ $2$ to $g (x)$ $g(x)$ , you get $f (x)$ $f(x)$ . This means that you're shifting the whole range of $g (x)$ $g(x)$ by $2$ $2$ .

Therefore, the range of $f (x)$ $f(x)$ is $[2, \infty)$ $[2,\infty)$ because that is what you get when you shift the range of $g (x)$ $g(x)$ , $[0, \infty)$ $[0,\infty)$ , by $2$ $2$ .

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

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

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