How do you graph #f(x)=abs(x-3)+4#?

Answer 1

Actually there are two graphs

#f(x)=(x-3)+4=x+1# for all values of #x>=3# and: #f(x)=-(x-3)+4=-x+7# for all values of #x<=3#
The #x=3# is important, as at that point #x-3# becomes negative and must be "saved" by the #abs#-function.
At the value of #x=3# the two functions meet at #(3,4)# graph{abs(x-3)+4 [-28.88, 28.85, -14.43, 14.45]}
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Answer 2

To graph the function ( f(x) = |x - 3| + 4 ), follow these steps:

  1. Identify the key features:

    • The function is in the form of ( |x - h| + k ), where ( h = 3 ) and ( k = 4 ).
    • The vertex of the absolute value function is at the point ((h, k)), which is ((3, 4)).
  2. Plot the vertex ((3, 4)) on the coordinate plane.

  3. Determine additional points to graph the function:

    • Choose values of ( x ) to the left and right of the vertex to find corresponding ( y ) values.
    • For example, let's use ( x = 1 ) and ( x = 5 ):
      • When ( x = 1 ): ( f(1) = |1 - 3| + 4 = 2 + 4 = 6 ), so plot the point ((1, 6)).
      • When ( x = 5 ): ( f(5) = |5 - 3| + 4 = 2 + 4 = 6 ), so plot the point ((5, 6)).
  4. Connect the plotted points with a straight line. Note that the absolute value function creates a "V" shape centered at the vertex.

Your graph should show a "V" shape with the vertex at ((3, 4)) and the arms extending upwards to ((1, 6)) and ((5, 6)).

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Answer from HIX Tutor

When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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