How do you graph #f(x) =abs(2x+3)#?
Please read the explanation.
Construct a table of values with Input:
Values are obtained for the graphs:
You can now analyze how the computed values reflect visually on their respective graphs.
Consider
This will help understand how transformations will work.
Graph of
This is the Parent Graph.
Graph of
Graph of
Let us find the
Let
Subtract 3 from both sides.
Divide both sides by
Hence,
Axis of Symmetry :
Domain is all possible x values:
Range:
Horizontal Shift:
Hope it helps.
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To graph the function ( f(x) = \lvert 2x + 3 \rvert ), follow these steps:

Identify key points:
 Find the xintercept by setting ( f(x) = 0 ) and solving for ( x ): ( 0 = \lvert 2x + 3 \rvert ) ( 2x + 3 = 0 ) ( x = \frac{3}{2} )
 Determine where the function changes direction, which occurs at ( x = \frac{3}{2} ) because the absolute value function ( \lvert 2x + 3 \rvert ) changes from negative to positive.

Create a table of values:
 Choose values of ( x ) around the key points found above. For example, you can choose ( x = 2, 1, 0, 1, 2 ).
 Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \lvert 2x + 3 \rvert ).

Plot the points from the table on a coordinate plane.

Draw the graph by connecting the points with a smooth curve. Remember that the graph should rise to the right of ( x = \frac{3}{2} ) and fall to the left.

Label the axes and any significant points on the graph.
This process will give you the graph of ( f(x) = \lvert 2x + 3 \rvert ).
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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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