Question

Can you please help me with 29 please list the end behaviors such as limits and as_,_

Answer 1

29. Given

`f(x)=(2x^2-32)/(6x^2+13x-5)`

The end behavior of the function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

- For local behavior of the function, see the graph of the function:

As it can be seen that the graph is moving towards positive infinity as x --> -5/2 + and x ---> 1/3 -

And towards negative infinity as x --> -5/2 - and x --> 1/3 +

Thus the local behavior of the function is:

Answer

`\begin{gathered} f(x)_{x\rightarrow-(5)/(2)^-}=-\infty \\ f(x)_{x\rightarrow-(5)/(2)^+}=\infty \\ f(x)_{x\rightarrow(1)/(3)^-}=-\infty \\ f(x)_{x\rightarrow(1)/(3)^+}=\infty \end{gathered}`

- For the end behavior of the function:

In words, we could say that as x values approach infinity, the function values approach y = 1/3 and as x values approach negative infinity, the function values approach y = 1/3. We can describe the end behavior symbolically by writing:

Answer

`\begin{gathered} as\text{ x}\rightarrow-\infty,f(x)\rightarrow(1)/(3) \\ as\text{ x}\rightarrow\infty,f(x)\rightarrow(1)/(3) \end{gathered}`