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 $Ag(ax+b)+B$.

1. How many parameters are introduced by such scaling?

1       2       3       4       5      

question id: parameters-a

2. 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

3. 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

4. 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

5. 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:

$$\begin{array}{}\text{(8.1)}& A{e}^{ax+b}+B\end{array}$$

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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