What is the graph of 1/x? and what are the domain and range?

Question

For some reason when I was taking notes today in calculus, I forgot to write this stuff down...help please anyone? first right will get 10 pts

Answer 1

The graph is called a hyperbola and it looks very cool.

domain : all reals except zero

range : all reals except zero

Good luck to you !

This is Algebra 2 stuff.  you may want to review it :)

Answer 2

go to www.coolmath.com/graphit and type the eqn in

it will draw it for u

the domains ia all real  numbers but not zero as that turns the denominator to zero and therefore u cant do 1/0.

p.s this is an algebra 1 question - ushould know this!!!!

Answer 3

Let f(x) = 1/x.

What can x not be equal to?

Right, we cannot divide by zero.

So the domain is all real numbers except zero.

What can f(x) not be equal to?

It can be positive (when x is positive).

It can be negative (when x is negative)

The limit of f(x) as x approaches 0  from the right is a positive infinity.

The limit of f(x) as x approaches 0 from the left is an negative infinity.

But, while the limit of f(x) as x approaches infinity (positive or negative) is zero, f(x) can never really equal zero.

So, the range is like the domain (all but zero).

To draw f(x):

1)  Draw you x and y axis system,

2)  Mark 1 and -1 on the x axis and the y axis.

3)  Lighly draw g(x) = x.

4)  Mark (1,1) and (-1, -1).

5)  Look at those limits mentioned above under range.  With x increasing from 1, f(x) swings down toward the x axis quickly and levels off without touching it.  Flip that over the g(x) diagonal for the f(x) as x goes from 0 to 1.  Now, flip that big U opening to the northeast (a hyperbola) over k(x) = - x so you have one in the first quadrant (both positive) and in the third quadrant (both negative).

Try a(x) = - 1/x.

Try b(x) = 1/x^2.