Graphing Families of Functions

[SKMC]

I have to prepare a graph of the family of functions: f(x) = -x^-n, for n = 1, n = 2, n = 3, for the range -2, 2.

I have produced the graph of the functions, but what is throwing me is that the last part of the question suggests i need to be very careful about where each function exists and whether the functions are positive or negative.

My understanding is that f(x) = -x^-n for n = 1 equals f(x) = - 1/x.

Can someone please tell me if this is correct? Or have I mistakenly made the function negative when it should be positive?

Many Thanks for your help.

 

[mmm4444bot]

I have produced the graph of the functions, but what is throwing me is that the last part of the question suggests i need to be very careful about where each function exists and whether the functions are positive or negative.

Hmmm. If you have already graphed the three functions, then you should already know where f(x) is positive or negative, as well as the domain for each function.

When you say that something is "throwing you", do you mean that you're not confident that your graphs are correct?

My understanding is that f(x) = -x^-n for n = 1 equals f(x) = - 1/x.

Can someone please tell me if this is correct?

Yes, that is correct. Your graph should show that -1/x is positive when x is negative, and -1/x is negative when x is positive, and zero is not in the domain.

 

[mmm4444bot]

f(x) = -x^(-n), for n = 1, n = 2, n = 3, for the range [-2, 2].

You meant to type "domain" instead of "range", yes?

 

[SKMC]

Yes I did mean that I wasn't confident that my graphs were correct. The question does say 'take x in the range (-2, 2)'

Thanks - really appreciate your help - your explanation matches exactly what i have graphed.

 

[mmm4444bot]

Yes I did mean that I wasn't confident that my graphs were correct.

Okay. If you do not have a grapher to check your work, you can find many web-based graphers using Google. HERE is one.

The question does say 'take x in the range (-2, 2)'

That's ambiguous instruction because the word "range" describes y values, not x values.

It would be better for the author to write something like "Graph over the interval [-2, 2]".

By the way, using interval notation, the "domain" for all three functions is written (-∞, 0) U (0, ∞).