The function ƒ(x) = 1/√(k² - x²) is defined for k as a positive constant, with the domain restricted to the interval (-k, k). To sketch the graph of this function, one must first understand the graph of √(k² - x²), which represents a semicircle. The reciprocal function, ƒ(x), will exhibit vertical asymptotes at x = -k and x = k, indicating that the function approaches infinity as x approaches these values.
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k is an unspecified constant - a parameter. k could be 1 or 2, but you shouldn't assume that it is any specific value.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.
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.
noahsdev, after you label some point k on the positive side, label another as -k on the negative side. 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.