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Graphing reciprocals of quadratic functions
- Lesson: 112:57
- Lesson: 212:02
- Lesson: 311:43
- Lesson: 410:25
Graphing reciprocals of quadratic functions
We have learnt the basics of reciprocal functions. In this section, we will learn how to graph the reciprocal of a quadratic function, while applying the same principles we used when graphing the reciprocal of a linear function, while following the "6-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) Plot vertex of the original function1
6) 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) Plot vertex of the original function1
6) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!
- 1.Given that f(x)=x2−9 , graph the reciprocal of the function f(x)
- 2.Given that g(x)=2x2+2x+1, graph the reciprocal of the function g(x)
- 3.Given that y=−2x2+x+1 , graph the reciprocal of y
- 4.Given that f(x)=−x2+2x−4 , graph the reciprocal of the function f(x)