Given:
The function
[tex]f(x)=\frac{2x+4}{3x+2}[/tex]
Required:
Find all parts.
Explanation:
Domain:
The domain of a function is the set of all possible inputs for the function.
Increasing and Decreasing of a function:
The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
Concavity:
A function f is concave up (or upwards) where the derivative f' is increasing. This is equivalent to the derivative of f', which is f'', being positive. Similarly, f is concave down (or downwards) where the derivative f' is decreasing (or equivalently, f'', is negative).
The graph of a function:
Now, the function defined on
[tex]=(-\infty,-\frac{2}{3})\cup(-\frac{2}{3},\infty)[/tex]
Where the function is not defined at A
[tex]A\text{ }is\text{ }x=-\frac{2}{3}[/tex][tex]\begin{gathered} \text{ For each of the following interval function is decreasing on}: \\ (-\infty,-\frac{2}{3})\cup(-\frac{2}{3},\infty). \end{gathered}[/tex]
Also,
[tex]\begin{gathered} \text{ Function is concave upward on }(-\frac{2}{3},\infty). \\ \text{ Function is concave downward on }(-\infty,-\frac{2}{3}). \end{gathered}[/tex]
Answer:
Completed the question.
