1. Use the

form to create a cubic function that (a) passes through the point and rises to

the right and (b) passes through the point and falls to the right. (There are

many correct answers.)

2. The

multiplicative inverse of is a complex number such that Find the multiplicative

inverse of each complex number.

3. Prove

that the product of a complex number and its complex conjugate is a real

number.

4. The

endpoints of the interval over which distinct vision is possible are called the

near point and far point of the eye (see figure). With increasing

age, these points normally change. The

1. Use the

form to create a cubic function that (a) passes through the point and rises to

the right and (b) passes through the point and falls to the right. (There are

many correct answers.)

2. The

multiplicative inverse of is a complex number such that Find the multiplicative

inverse of each complex number.

3. Prove

that the product of a complex number and its complex conjugate is a real

number.

4. The

endpoints of the interval over which distinct vision is possible are called the

near point and far point of the eye (see figure). With increasing

age, these points normally change. The table shows the approximate near points

(in inches) for various ages (in years).

(a) Use the regression feature

of a graphing utility to find a quadratic model for the data. Use a graphing utility

to plot the data and graph the model in the same viewing window.

(b) Find a rational model for the

data. Take the reciprocals of the near points to generate the points

Use the regression feature

of a graphing utility to find a linear model for the data. The resulting line

has the form Solve for Use a graphing utility to plot the data and graph the

model in the same viewing window.

(c) Use the table feature of

a graphing utility to create a table showing the predicted near point based on each

model for each of the ages in the original table. How well do the models fit

the original data?

(d) Use both models to estimate

the near point for a person who is 25 years old. Which model is a better fit?

(e) Do you think either model can

be used to predict the near point for a person who is 70 years old? Explain

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