29. Given
[tex]f(x)=\frac{2x^2-32}{6x^2+13x-5}[/tex]
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
[tex]\begin{gathered} f(x)_{x\rightarrow-\frac{5}{2}^-}=-\infty \\ f(x)_{x\rightarrow-\frac{5}{2}^+}=\infty \\ f(x)_{x\rightarrow\frac{1}{3}^-}=-\infty \\ f(x)_{x\rightarrow\frac{1}{3}^+}=\infty \end{gathered}[/tex]
- 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
[tex]\begin{gathered} as\text{ x}\rightarrow-\infty,f(x)\rightarrow\frac{1}{3} \\ as\text{ x}\rightarrow\infty,f(x)\rightarrow\frac{1}{3} \end{gathered}[/tex]
