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 8.1 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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