Pre Calculus: Week 13, Reciprocals of Linear Functions

This week in Pre calc 11 we learned how to graph Reciprocals of Linear Functions.

Reciprocal functions are graphed with  y= \frac{1}{x}

How to graph a Reciprocals of Linear Functions

Step 1:  Graph the original Linear function

Step 2:  Find the Invariant Points (The Invariant Points are where the line meets  y= -1 and y=1. )

Step 3: Find the Asymptotes and draw in dashed lines for both. There is a vertical and horizontal one. This is an imaginary line in which a graph reciprocal function will approach but will never reach. The vertical asymptote for the line will be in the middle of the two Invariant Points. The Invariant Points are where the line meets  y= -1 and y=1.

Step 4:  Draw the hyperbola.

Let’s take -2x +5 and \frac{1}{-2x + 5} for example

  • The horizontal asymptote is y=0
  • The vertical asymptotes is x = 2.5
    • A thing to notice when trying to find the vertical asymptote is that it is where the original line’s x axis is.
    • It is also in the middle of the two invariant points

The invariant points would be (2, 1) and (3, -1)

Things you will have to define for  \frac{1}{-2x + 5}

  • x intercept : none the reciprocated function does not cross the x axis because there is a horizontal asymptote
  • y axis: y= 0.2
  • Domain: XER,  x\neq 2.5
  • Range: YER, y\neq 0
  • Asymptotes:
    • horizontal : y = 0
    • vertical : x = 2.5

This is how you would graph Reciprocals of Linear Functions.


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