Question

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Which answers describe the end behaviors of the function modeled by the graph?



f(x)=−3^(x+2)−2


Select each correct answer.




As x increases without bound, f(x) increases without bound.



As x decreases without bound, f(x) approaches the line y=−2.



As x increases without bound, f(x) approaches the line y=−2.



As x increases without bound, f(x) decreases without bound.


This is a multiple choice question, so there might be 2 answers.

Answer 1

Answer:

Option B and D are correct.

Step-by-step explanation:

Given the function: $y=f(x) = -3^{x+2}-2$

End behavior states that  a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.

As $x \rightarrow \infty$ in the given function, then $f(x) \rightarrow -\infty$

and

As $x \rightarrow -\infty$ in the given function, then $y=-2$

Therefore, as x increases without bound , f(x) decreases without bound

and as x decreases without bound , f(x) approaches the line y =-2