Question

A rational function is a function that can be written in the form
f ( x ) = g ( x ) h ( x )
where
h ( x ) ≠ 0
.
The most basic rational function is
f ( x ) = 1 x
, where
x ≠ 0
. This is called the parent rational function.
Use the Desmos
(Links to an external site.)
activity to explore the function
f ( x ) = 1 x
. Take a close look at the table of values as well. Use any noticings to respond to the following questions:
What seems to be happening to the graph as it gets closer to 0 from the left side?
What seems to be happening to the graph as it gets closer to 0 from the right side?
Is the graph always increasing, always decreasing, or a combination of both? Explain how you know.
Where, if anywhere, do you think the graph crosses the y-axis? Explain how you know.
Where, if anywhere, do you think the graph crosses the x-axis? Explain how you know.

Answer 1

the graph of the function drops if we walk on the left side. If you walk on the right side, it increases.the graph increasing, and decreasing, so a combination of both, because it is located in mirror planes. The function does not intersect the axis Ox and Oy, because y≠ 0 (1/x≠ 0), and x≠0