How to Sketch the Function ƒ(x) = 1/√(k2-x2)?

[noahsdev]

Homework Statement

Consider the function ƒ:-k,k→R, where ƒ(x) = 1/√(k²-x²), where k is a positive constant.
(i) Sketch the graph of y = ƒ(x)
(ii) What is the domain of the function?

Homework Equations

ƒ(x) = 1/√(k²-x²)

The Attempt at a Solution

I don't understand how I am supposed to solve this. Couldn't k equal anything? Why couldn't it be 1 or 2? This makes no sense.
Help is appreciated. Thanks.

 

[Mark44]

Homework Statement

Consider the function ƒ:-k,k→R, where ƒ(x) = 1/√(k²-x²), where k is a positive constant.
(i) Sketch the graph of y = ƒ(x)
(ii) What is the domain of the function?

Homework Equations

ƒ(x) = 1/√(k²-x²)

The Attempt at a Solution

I don't understand how I am supposed to solve this. Couldn't k equal anything? Why couldn't it be 1 or 2? This makes no sense.
Help is appreciated. Thanks.

k is an unspecified constant - a parameter. k could be 1 or 2, but you shouldn't assume that it is any specific value.

Can you sketch the graph of y = $\sqrt{k^2 - x^2}$? If you can get this graph, then the graph of f is just the reciprocal.

 

[LCKurtz]

I don't understand how I am supposed to solve this. Couldn't k equal anything? Why couldn't it be 1 or 2? This makes no sense.
Help is appreciated. Thanks.

Just draw an x axis, mark some point on the positive side, and label it k. Then draw your graph.

 

[Mark44]

Just draw an x axis, mark some point on the positive side, and label it k. Then draw your graph.

noahsdev, after you label some point k on the positive side, label another as -k on the negative side. Then draw your graph.