Question

Consider the funtion f(x) = 1/x. Which of the following statements are true?

Check all that apply.

a. f is increasing on the interval (1, infinite)
b. f is decreasing on the interval [2, infinite)
c. f has a miximum on the interval [2, infinite)
d. f has a miximum on the interval (1, inifinte)
e. f has a mimimum on the interval [2, infinite)

Answer 1

easiest way to get started on a problem like this is to graph a few points and see how the function behaves. Since the widest interval you need to observer is from [1, infinity) I would graph the points x=1 x=1/2 x=2 and a few more until you see what the function does.

Answer 2

It goes straight across?

Answer 3

horizontally

Answer 4

ok try this, when x = 1 y= ?

Answer 5

1?

Answer 6

yup. When x = 2 y = ?

Answer 7

2?

Answer 8

the function is 1/x , so, that means to find out where the point is on the graph of a specific x, you just plug that number into the x in the function. so, x=1 , the y= 1/1 which is 1. If x=2, then y = 1/{2} and so forth.

Answer 9

So you can pretty easily sketch a graph by just picking whatever x values you want, and then finding the corresponding y value. Like so.