How do you graph, find the zeros, intercepts, domain and range of $f (x) = | x + 2 | - | x |$ $f(x)=abs(x+2)-absx$ ?

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How do you graph, find the zeros, intercepts, domain and range of $f (x) = | x + 2 | - | x |$ $f(x)=abs(x+2)-absx$ ?

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Answer 1 · 2017-04-05T04:59:14

Domain is $(- \infty, \infty)$ $(-oo,oo)$ , range is $[- 2, 2]$ $[-2,2]$ .

$y$ $y$ -intercept is $2$ $2$ and $x$ $x$ -intercept is $x = - 1$ $x=-1$

Explanation:

For $x \leq - 2$ $x<=-2$ ,

$f (x) = - (x + 2) - (- x) = - x - 2 + x = - 2$ $f(x)=-(x+2)-(-x)=-x-2+x=-2$

for $x \geq 0$ $x>=0$ ,

$f (x) = (x + 2) - (x) = x + 2 - x = 2$ $f(x)=(x+2)-(x)=x+2-x=2$

and for $- 2 < x < 2$ $-2<x<2$ $f (x) = x + 2 - (- x) = 2 x + 2$ $f(x)=x+2-(-x)=2x+2$

Hence domain is $(- \infty, \infty)$ $(-oo,oo)$ , range is $[- 2, 2]$ $[-2,2]$

and for $x = 0$ $x=0$ i.e. $y$ $y$ -intercept is $2$ $2$ and $x$ $x$ -intercept being at $y = 0$ $y=0$ , is given by $2 x + 2 = 0$ $2x+2=0$ i.e. $x = - 1$ $x=-1$

The graph appears as follows:

graph{|x+2|-|x| [-10, 10, -5, 5]}

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How do you graph, find the zeros, intercepts, domain and range of $f (x) = | x + 2 | - | x |$ $f(x)=abs(x+2)-absx$ ?

1 Answer

Explanation:

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Science

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Humanities

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How do you graph, find the zeros, intercepts, domain and range of f(x)=|x+2|−|x|f(x)=abs(x+2)-absx?

1 Answer

Explanation:

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Impact of this question

How do you graph, find the zeros, intercepts, domain and range of $f (x) = | x + 2 | - | x |$ $f(x)=abs(x+2)-absx$ ?