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Chap 2 Exercises
\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]
Exercise 1 Here are some function definitions in the format we will use in this book. For each, say what is the name of the function being defined, what are the names of the inputs to the function, and what are the names, if any, of the parameters used in the definition.
- \(h(x) \equiv 3 x + 2\).
What is \(x\)?
- \(\text{line}(x) \equiv m x + b\)
What is \(m\)?
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What is \(b\)?
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- \(\text{wave}(t) \equiv A \sin(2 \pi t/ P)\)
What is “wave”?
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What is \(t\)?
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What is \(P\)?
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What is \(\sin\)?
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- \(\text{plane}(x, y) \equiv a + bx + cy\)
What is \(a\)?
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- \(f_1(z) = z^n\)
What is \(n\)?
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Exercise 2 Keeping in mind the notation style we use in MOSAIC Calculus, which of these things is a function? Which a number?
- What kind of a thing is \(\sqrt{z\,}\) ?
A function
A number
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- What kind of a thing is \(\sqrt{y^\star\,}\) ?
A number
A function
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- What kind of a thing is \(e^{k t}\)?
A function
A number
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- What kind of a thing is \(k\) in the definition \(g(k) \equiv e^k\)?
A number
The name of an input to a function.
A function
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