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- Reciprocal Functions
Graphing reciprocals of linear functions
- Intro Lesson35:38
- Lesson: 113:25
- Lesson: 211:25
- Lesson: 312:16
- Lesson: 413:14
- Lesson: 511:48
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 at y=0
2) Plot vertical asymptote(s) equate the original function to 0; solve for x
3) Plot y-intercept(s) y-intercept(s) of the original function1
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!
1) Plot a horizontal asymptote at y=0
2) Plot vertical asymptote(s) equate the original function to 0; solve for x
3) Plot y-intercept(s) y-intercept(s) of the original function1
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!
- IntroductionGraph f(x)=x1
- 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=21−5x , graph the reciprocal of y
- 5.Given that y=31−9x , graph the reciprocal of y