Graphing reciprocals of linear functions

Intro Lesson
35:38
Lesson: 1
13:25
Lesson: 2
11:25
Lesson: 3
12:16
Lesson: 4
13:14
Lesson: 5
11:48

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Graphing reciprocals of linear functions

We know that taking the reciprocal of a very large number will grant us a very small number. Conversely, if we take the reciprocal of a very small number, we will obtain a very small number. What will happen if we take the reciprocal of a linear function? In this section, we will learn about the concept behind the reciprocal of a linear function, as well as how to graph it, while following the "5-steps Approach" noted below.

Lessons

Steps to graph the reciprocal of a function:
1) Plot a horizontal asymptote

y=0

2) Plot vertical asymptote(s)

equate the original function to 0; solve for

x

3) Plot y-intercept(s)

\frac{1}{\text {y-intercept(s) of the original function}}

4) Plot invariant points:

equate the original function to +1 and -1; solve for

x

5) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!

Introduction
Graph $f(x)= \frac{1}{x}$

1.
Given that $f(x)=4x$ , graph the reciprocal of function $f(x)$

2.
Given that $f(x)=x+5$ , graph the reciprocal of function $f(x)$

3.
Given that $f(x)=2x-1$ , graph the reciprocal of the function $f(x)$

4.
Given that $y= \frac{1}{2}-5x$ , graph the reciprocal of $y$

5.
Given that $y=\frac{1}{3}-\frac{x}{9}$ , graph the reciprocal of $y$

Graphing reciprocals of linear functions

Graphing reciprocals of linear functions

Lessons

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