8  Parameters

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8.1 Reading questions

Reading question 8.1 Input scaling shifts and scales one axis. Which one?

the horizontal axis       the vertical axis      

question id: input-scaling

Reading question 8.2 Input and output scaling transform a function such as \(g(x)\) into a new function \(A g(a x + b) + B\).

  1. How many parameters are introduced by such scaling?
1       2       3       4       5      

question id: parameters-a

  1. Which are the parameters involved in input scaling?
Just A       A and B       A and a       B and b       a and b      

question id: parameters-b

  1. 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

  1. 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

  1. 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

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