(a).

Observe the table :

Graph:

Observe the table and plot the ordered pairs .

(b)

Determine whether the given function is linear or non linear.

First compute the average rate of change of  with respect to  and then compute the ratio of the consecutive outputs.

If the average rate of change is constant, then the function is linear else non-linear.

Average rate of change

\                     \                                                                   \                   \                                                                       \                  \                              \                                \                                           \                 \

Observe the table.

For the function, the average rate of change is .

Since the average rate of change is constant , the function is a linear function.

(c).

Definition of the slope :

If the average rate of change of the function is constant then slope of the line is the average rate of change of the function.

Slope of the linear function is .

The slope of the function is .

Consider the point .

The general form of linear function is when the point is and slope .

Substitute and inthe function .

.

The linear function is .

(d).

The linear fucntion is .

The price of the function is not negative and quantity of the function should noe be negative,then .

The Domain of the function is or .

(e).

Graph:

Graph for the linear function in cartesian plane.

(f).

The linear fucntion is .

Slope of the linear function is .

If the hot dogs increases $ then the  sodas purchased decreases to .

(g).

The linear fucntion is .

Find the - intercept by substituting   in the function .

The -intercept is .

- intercept : When the price is , sodas will be demanded.

For finding intercept ,when   in the function .

-intercept : When the sodas , the price is .

(a)

(b) The average rate of change of the function is constant, hence the given function is linear.

(c) .

(d) The Domain of the function is  or .

(e)

Graph of the linear function : 

(f). If the hot dogs increases $ then the  sodas purchased decreases to  .

(g)

- intercepts : When the price is , sodas will be demanded.

intercepts: When the sodas ,the price is .