Graphing Reciprocal Functions 1

Hey everyone! :) So yesterday, we learned how to graph reciprocal functions.


There are two different shapes.

Basic Shape: f(x)= 1/x
Shifted Shape: f(x)= 1/x-h+k

If the graph is shifted, read horizontal shifts (h values), as opposite as given and read the vertical shifts (k values), as is. If there is no bracket around the x-h, act as if there is a bracket.

- There will be an asymptote at the value for x that makes the function undefined- that is called a vertical asymptote (VA). In basic form, the VA is always at x=0.

- There is also an asymptote at the value for y that is no longer able to occur due to the unacceptable value for x (VA)- this is called a horizontal asymptote (HA). In basic form, the HA is always at y=0.

- If the graph is shifted, the vertical asymptote (VA), will always be at x=h and the horizontal asymptote (HA) will always be at y=k.

- To sketch the graph, we need to have at least three points on either side of the VA.

- To find the x-intercept- make y=0 and solve for x.
- To find y-intercept- make x=0 and solve for y.

- If a negative is placed in front of the function, this means to multiply all of the y-values by -1.

Here is an example below:

f(x)= 1/x

Vertical Asymptote (VA) x=0

Horizontal Asymptote (HA) y=0

Domain: x ∊R, x≠0
Range: y∊R, y≠0

x-intercept: none

y-intercept: none

So, I hope that this was okay enough. This is my first time blogging and I hope that everyone in having a good weekend. See you all on Monday! :)