question id: input-scaling
8 Parameters
\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]
8.1 Reading questions
Reading question 8.1 Input scaling shifts and scales one axis. Which one?
Reading question 8.2 Input and output scaling transform a function such as \(g(x)\) into a new function \(A g(a x + b) + B\).
- How many parameters are introduced by such scaling?
question id: parameters-a
- Which are the parameters involved in input scaling?
question id: parameters-b
- How does the parameter \(b\) move the axes?
Moves the horizontal axis left-or-right.
Moves the vertical axis up-or-down.
Shrinks or stretches the horizontal axis.
Shrinks or stretches the vertical axis.
question id: parameters-c
- How does the parameter \(B\) move the axes?
Moves the horizontal axis left-or-right.
Moves the vertical axis up-or-down.
Shrinks or stretches the horizontal axis.
Shrinks or stretches the vertical axis.
question id: parameters-d
- What does the parameter \(a\) do?
Moves the horizontal axis left-or-right.
Moves the vertical axis up-or-down.
Shrinks or stretches the horizontal axis.
Shrinks or stretches the vertical axis.
question id: parameters-e
Reading question 8.3 The exponential function with input and output scaling might look like this:
\[ A e^{a x + b} + B \tag{8.1}\]
However, the algebraic properties of exponentials are such that one of the four parameters in Math expression eq-expon-scaled is redundant. Which one is it?
\(a\) is redundant with \(A\).
\(b\) is redundant with \(A\).
\(a\) is redundant with \(B\).
\(b\) is redundant with \(B\).
question id: exponential-scaling