The general equation of the sine function y=f(x) is defined as
where A is the Amplitude
B represents the frequency of the function with period equals
C represents the Horizontal shift, For Phase shift= -C/B
D represents the Vertical shift.
The data given that the amplitude of the function A=6
Vertical shift
Horizontal Shift
Now plug in in the general equation of sine function, we get
The function with the same end behavior of f(x) is the last option:
<h3>Which function has the same end behavior of f(x)?</h3>
By looking at the graph, we can see that the end behavior of f(x) is:
as x → ∞; f(x) → -∞
as x → -∞; f(x) → ∞
Then we just want a function that depends linearly with x and that has a negative coefficient.
The correct option is the last one:
Where clearly, when x tends to infinity the function tends to negative infinity, and when x tends to negative infinity, the function tends to infinity.
If you want to learn more about end behavior:
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