Exam 1: Functions, Graphs, and Models; Linear Functions

Let y=-9 x+221 represent the number of students present in a large class, where x represents the number of hours of study required weekly. What is the rate of change of the number of students in the class with respect to the number of hours of study?

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 400 parts are produced, the cost is $2700. What is the marginal cost of The function?

A small toy company that only makes action figures is owned by its stockholders. The dividend per share of stock is a function of the number of action figures it sells and is defined by $\mathrm { D } ( \mathrm { x } ) = \frac { \$ 4.46 \mathrm { x } - \$ 270 } { 3949 }$ , where x is the Number of action figures sold. What is the dividend for each share of stock if 1350 action figures are sold?

The number N, in millions of Americans of age x with arthritis, is estimated with the following graph. Give the age(s) at which there are 2 million people with arthritis.

State whether the graph is or is not that of a function. -

An electrician charges a fee of $\$ 45$ plus $\$ 30$ per hour. Let $y$ be the cost in dollars of using the electrician for $x$ hours. Find the slope-intercept form of the equation.

Decide whether or not the set of ordered pairs defines a function. - $\{ ( - 3 , - 5 ) , ( - 1,2 ) , ( 2 , - 3 ) , ( 7,2 ) \}$

Decide whether the slope is positive, negative, zero, or undefined. -

Find the x- and y-intercepts of the graph of the given equation, if they exist. Then graph the equation. - $2 y = \frac { 3 } { 5 } x$

Find the rate of change. Use appropriate units.

The profit for a product is given by the function $P ( x ) = 35 x - 1086$ , where $x$ is the number of units produced and sold. Find the marginal profit for the product.

Determine whether or not the relationship shown in the table is a function. - x 1 3 5 8 11 y 8 1 4 8 -3 Does the table define x as a function of y?

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of tuition at a community college is given $C ( x ) = 467 + 69 x$ x, where x is the number of credit hours.

The following graph shows the stock price of a new internet company over the first 18 months after the initial public offering of its stock. How many months was the stock price $40 during the initial 18 month period?

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The height of an object $t$ seconds after being dropped from an altitude of 249 feet is given by the function h(t) = $- 16 t ^ { 2 } + 249$

Find the slope of the line through the pair of points. - $( 7 , - 3 )$ and $( - 5,6 )$

Graph the function with a graphing utility. - $y=x^{3}-1$

The number of shares s of a certain stock traded on a given day x.

A cable TV company charges $\$ 24$ for the basic service plus $\$ 8$ for each movie channel. Let y be the total cost in dollars of subscribing to cable TV, using $x$ movie channels. Find the slope-intercept form of the equation.

Find the slope of the line. -