How do you graph f(x)=|x|+|x+2|?

1 Answer
Sridhar V.
Jan 31, 2018

Please read the explanation.

Explanation:

Given:

y=f(x)=|x|+|x+2|

We need to graph this absolute value function.

We will assign the values for x as follows and find the corresponding y value.

x:+4,+3,+2,+1, 0, −1,−2,−3,−4

To find the corresponding y value, we will substitute (in order) the values of x in

y=|x|+|x+2|

Please look at the table of values that contains all values for xandy: and also as Ordered Pair to facilitate graphing.

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The corresponding graph is given below:

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Observations:

For the parent function f(x)=|x|,

Vertex is at (0,0)

Vertex is the minimum point on the graph.

Axis of Symmetry is at x=0

A translation is a transformation that shifts a graph horizontally or vertically, but does not change the orientation of the graph.

Please refer to the graph to observe the following:

Domain of the function

y=f(x)=|x|+|x+2|

is (−∞,∞)

Range of the function

y=f(x)=|x|+|x+2|

is [2,∞), since f(x)≥2

Extreme Points are none for f(x)

Critical Points:

Critical points are points where the function is defined and its derivative is zero or undefined.

Critical Points are at x=−2,x=0

X and Y Intercepts:

x-axis interception points of f(x)=|x|+|x+2|: None

y-axis interception points of f(x)=|x|+|x+2|:(0,2)

The graph of y=f(x)=|x|+|x+2|

has shifted up (a.k.a. Vertical Translation) by two units comparing to the graph of the parent function

y=f(x)=|x|

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