How do you graph $y = | x | - 4$ $y= absx- 4$ ?

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How do you graph $y = | x | - 4$ $y= absx- 4$ ?

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Answer 1 · 2015-04-01T20:11:30

Start by graphing (or thinking of the graph of) $y = | x |$ $y=absx$ .

graph{abs (x) [-10, 10, -5, 5]}

Now, for $y = | x | - 4$ $y=abs(x) - 4$ the equations says "find the absolute value of x and then subtract 4 from that number".

So for every $x$ $x$ value, we find the number (point) $y = | x |$ $y = absx$ and the change $y$ $y$ by subtracting $4$ $4$ . This gives us a new point that is a distance of $4$ $4$ lower than the old point. The end result is, we will move the entire graph down $4$ $4$ .

graph{abs (x) -4[-10, 10, -5, 5]}

Answer 2 · 2015-04-01T20:12:08

step1:
Use the definition that $| x | = x$ $|x| = x$ for $x \geq 0$ $x >=0$
and that $| x | = - x$ $|x| = -x$ for $x < 0$ $x<0$

This means, given that,
$y = | x | - 4$ $y = |x| - 4$ this graph is equivalent to the two lines below,

$y = x - 4$ $y = x - 4$ , $x \geq 0$ $x>=0$
$y = - x - 4$ $y = -x - 4$ , $x < 0$ $x< 0$

Note that $y = x - 4$ $y = x - 4$ only when $x \geq 0$ $x>=0$ and

$y = - x - 4$ $y = -x - 4$ only when $x < 0$ $x< 0$

Graph these two lines and you shall get the graph for y = |x| - 4

Don't forget the limitations of each line!

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How do you graph $y = | x | - 4$ $y= absx- 4$ ?

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