# Thread: how to figure out these question?

1. ## how to figure out these question?

1. f(x)=(x-4)^（2/3）

2. f(x)= (x² - 1)/x³

3. f(x)= ( x³ - x² - 1)/(x - 1)

sketch a graph of the function and find

domain
x-intercepts
y-intercept
local extrema
intervals where increasing
intervals where decreasing
intervals where concave upward
intervals where concave downward
inflection points

2. Originally Posted by ijoe
1. f(x)=(x-4)^（2/3）

2. f(x)= (x² - 1)/x³

3. f(x)= ( x³ - x² - 1)/(x - 1)

sketch a graph of the function and find

domain
x-intercepts
y-intercept
local extrema
intervals where increasing
intervals where decreasing
intervals where concave upward
intervals where concave downward
inflection points
a) Domain: the domain is simply all the number in the x-axis in which the function is defined. Make sure you point out where it's not defined. So for example, for number 2:

$\displaystyle Domain: \left\{X\in R| X\neq0\right\}$ << because you cannot divide by 0.

b)X-interecepts: Find he roots of the function. Set it equal to zero and solve for x.

c)Y-intercepts: Set your X's equal to 0 and solve for Y.

d,e and f) Get the derivative of the function and set it equal to zero. Solve for the X's and those will be your critical points/local extrema. Then, make a table of the Intervals of Increase and Decrease. Pick numbers in between the critical points and evaluate them in the derivative. If they're positive, then the function is increasing in that interval in between those two critical points. If it's negative, then it's decreasing.

g, h and i) Get your second derivative and set it equal to 0 and solve for the X's. Those will be your Inflection Points. Then make a Table of Concavity. Pick number in between the Inflection Points and evaluate them using the second derivative. If it's positive, then the function is concave up in those intervals between the two inflection points. If it's negative, then it's concave down.

Using all this information, you can probably graph the function but you must also need the horizontal and vertical asymptotes (and oblique, if any).

Cheers!