Functions/graphs

[Lemonmelon]

Could anyone help with the following questions?

What is the domain and range of the function f(x) = x/(x^2 - 4) ?
The domain is all real x, x not equal to + or - 2, I'm not sure how to work out the range from this

Scetch y = x - 1/(x^2 - 5)
the x intercepts are + or - root 5 and the y intercept is 1/5. The answer presents the graph as odd, but I calculated it as neither odd nor even. I'm not quite sure how to work out the shape of the graph.

 

[Deleted member 4993]

Could anyone help with the following questions?

What is the domain and range of the function f(x) = x/x^2 - 4 ?

Scetch y = x - 1/x^2 - 5

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

What is the domain and range of the function f(x) = x/x^2 - 4 ?

What you have posted means this:

. . . . .\(\displaystyle f(x)\, =\, \dfrac{x}{x^2}\, -\, 4\, =\, \dfrac{1}{x}\, -\, 4\)

I will guess that you mean the following:

. . . . .\(\displaystyle f(x)\, =\, \dfrac{x}{x^2\, -\, 4}\)

...which would by typed as "f(x) = x / (x^2 - 4)". (To learn how to type math as text, try here.)

To learn how to find domains and ranges, try here. In this particular c case, you'll need to account for zeroes in the denominator.

Sketch y = x - 1/x^2 - 5

What you have posted means this:

. . . . .\(\displaystyle y\, =\, x\, -\, \dfrac{1}{x^2}\, -\, 5\)

I suspect, however, that you mean the following:

. . . . .\(\displaystyle y\, =\, \dfrac{x\, -\, 1}{x^2\, -\, 5}\)

To learn how to graph rational functions, try here.

Once you have studied the lessons at the links, please attempt the exercises. If you get stuck, please reply showing all of your thoughts and efforts. Thank you!