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How do you graph #1/2sin(x-pi)#?

Answer 1

Observing the equation of your function you can deduce a lot of things.
Considering: #y=1/2sin(1*x-pi)# you have a sine curve with:

1]
The #1# in front of #x# (indicated as #k#) allows you to evaluate the length #lambda# of your sine curve; #k=(2pi)/lambda# or #1=(2pi)/lambda# and #lambda=2pi#;

2]
The #1/2# is the Amplitude of your sine curve (maximum height);

3]
#-pi# in the argument of #sin# means that your sine is "moved" starting at a value that is #sin(-pi)# when #x=0#; consequently it will start not "going up" as the normal sine functions but down:

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Answer 2

Samantha Abate

To graph the function ( \frac{1}{2}\sin(x - \pi) ), follow these steps:

Start by graphing the parent function ( y = \sin(x) ).
Apply transformations to the parent function based on the given equation:
- The coefficient ( \frac{1}{2} ) vertically stretches the graph by a factor of ( \frac{1}{2} ).
- The term ( x - \pi ) horizontally shifts the graph to the right by ( \pi ) units.
Plot key points on the transformed graph by considering the key points on the parent function and applying the transformations.
Connect the plotted points smoothly to sketch the graph of ( y = \frac{1}{2}\sin(x - \pi) ).

Ensure that you accurately apply the transformations to obtain the final graph.

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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.