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

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The function ƒ(x) = 1/√(k² - x²) is defined for x in the interval (-k, k), where k is a positive constant. To sketch the graph, one should first understand the shape of the function √(k² - x²), which represents a semicircle, and then take its reciprocal. The domain of the function is restricted to values of x that keep the expression under the square root positive, specifically within the interval (-k, k). The discussion emphasizes that k can be any positive value, but it is treated as a parameter rather than a specific number. Properly sketching the graph involves marking points at k and -k on the x-axis and drawing the corresponding curve.
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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.
 
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noahsdev said:

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.
 
noahsdev said:
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.
 
LCKurtz said:
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.
 

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