Respuesta :

mixter17

Hello!

We have to remember that absolute value functions have the following form:

[tex]f(x)=|x|\left \{ {{x,if}x\geq0 \atop {-x,if}x<0} \right.[/tex]

It means that there is a positive and a negative slope lines,

Let's find the information that we need to graph a absolute value function:

First:

Finding the y-intercept,

[tex]f(0)=2(0)+2=2[/tex]

So, the y-intercept is (0,2)

Second:

Finding the two lines intercepts,

if x ≥ 0

[tex]y=2*(x)+2=2x+2[/tex]

if x< 0

[tex]y=2*(-x)+2=-2x+2[/tex]

Therefore,

If [tex]y=y[/tex] , we have that:

[tex]-2x+2=2x+2\\2-2=2x+2x\\0=4x\\x=0[/tex]

[tex]f(0)=-2(0)+2=2\\y=2[/tex]

So, both lines intercepts at (0,2).

Ver imagen mixter17
wiseowl2018

Answer:

The graph is shown as under

Step-by-step explanation:

y = | x | + 2

Finding the absolute value vertex.

In this case, the vertex for  y = | x | + 2  is  ( 0 , 2 ) .  ( 0 , 2 )

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

( − ∞ , ∞ ) { x | x ∈ R }

For each  x value, there is one  y  value. Select few  x  values from the domain. It would be more useful to select the values so that they are around the  x  value of the absolute value vertex.

Ver imagen wiseowl2018

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