How do you graph # f(x) = x + x + 2 #?
Please read the explanation.
Given:
We need to graph this absolute value function.
We will assign the values for
To find the corresponding
Please look at the table of values that contains all values for
The corresponding graph is given below:
Observations:
For the parent function
Vertex is at
Vertex is the minimum point on the graph.
Axis of Symmetry is at
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
is
Range of the function
is
Extreme Points are none for
Critical Points:
Critical points are points where the function is defined and its derivative is zero or undefined.
Critical Points are at
X and Y Intercepts:
xaxis interception points of
yaxis interception points of
The graph of
has shifted up (a.k.a. Vertical Translation) by two units comparing to the graph of the parent function
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To graph ( f(x) = x + x + 2 ), follow these steps:

Identify the critical points by setting the absolute values equal to zero and solving for ( x ). ( x = 0 ) when ( x = 0 ). ( x + 2 = 0 ) when ( x = 2 ).

Determine the intervals between the critical points (∞, 2), (2, 0), and (0, ∞).

Choose a test point from each interval to determine the sign of ( f(x) ).

Substitute the test points into the original function ( f(x) = x + x + 2 ) to find the corresponding ( f(x) ) values.

Plot the critical points and the points where the function changes direction.

Sketch the graph connecting the points smoothly.
The resulting graph will be Vshaped with the vertex at (2, 0), opening upwards, and another vertex at (0, 2), also opening upwards.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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