1. Use the form to create a cubic function that (a) passes through the point and rises to the right.

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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