Math Help:Reciprocal & Graphing

  • Thread starter Raza
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In summary, the reciprocal of A) y=x^2 is y=\frac{1}{x^2}, and the reciprocal of B) y=\sqrt{x} is y=\sqrt{\frac{1}{x}}. To graph these functions, you will need to pick a relevant domain and plot the corresponding points on a graph. However, it is unclear if you are supposed to find the inverse function or the reciprocal for this problem. Please clarify with your teacher or instructor.
  • #1
Raza
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What would be the reciprocal of the following:

[tex]A)y=x^2[/tex]

[tex]B)y=\sqrt{x}[/tex]

I think the reciprocal for A, it would be:

[tex]y=\frac{1}{x^2}[/tex]

And B would be:

[tex]y=\sqrt{\frac{1}{x}}[/tex]

And also, How would I graph this?
I just need the table of values. Well, I need to do domain,range,graphing and a summary but I think I can do that myself if I get how to do the table of values.


Thanks :smile:
 
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  • #2
If you are talking about reciprocals of numbers, then yes, the reciprocals of [itex]x^2~and~`\sqrt(x)~are~\frac{1}{x^2}~and~\frac{1}{\sqrt(x)}[/itex]

Since no domain has been provided in the question, you have to come up with what you think will be a relavant domain- ie : one which includes any "important" behavior.

For [itex]y = x^2 [/itex], I would pick a bunch of numbers say, from the set [-10, 10].
 
  • #3
oops - lol nvm.
 
  • #4
Would this be the graph:
GraphReciprocal.jpg


The blue one is [tex]\frac{1}{x^2}[/tex] and the red one is [tex]\sqrt{\frac{1}{x}}[/tex]
 
  • #5
One question: since if f(x)= x2 (for x>= 0), then f-1(x)= &sqrt;(x) are the functions you give, are you sure it is "reciprocal" that is intended rather than the inverse function?
 
  • #6
I don't get your question. Please rephrase it.
 
  • #7
Raza said:
I don't get your question. Please rephrase it.

He means are you sure you're meant to be doing 1/y or should you be finding the inverse function (eg. the inverse of multiplication is division, the inverse of squaring is square rooting)?
 
  • #8
I am sure that I don't have to find the inverse function.
 
Last edited:

1. What is the definition of a reciprocal?

A reciprocal is the inverse of a number. It is found by dividing 1 by the original number. For example, the reciprocal of 2 is 1/2.

2. How do I find the reciprocal of a fraction?

To find the reciprocal of a fraction, switch the numerator and denominator. For example, the reciprocal of 2/3 is 3/2.

3. What is the importance of knowing how to find reciprocals?

Finding reciprocals is important in many mathematical operations, such as dividing fractions and solving equations involving fractions. It also helps in simplifying complex fractions.

4. What is the process for graphing a reciprocal function?

To graph a reciprocal function, start by plotting the x and y-intercepts. Then, find additional points by plugging in different values for x. Finally, connect the points with a smooth curve.

5. How do I know if a graph represents a reciprocal function?

A graph represents a reciprocal function if it is a hyperbola, which is a curved line with two branches that approach the x and y-axes but never meet them. The equation of a reciprocal function is y = 1/x.

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