Exam 3: Functions and Graphs

The owner of an ice cream franchise must pay the parent company $1,100 per month plus 5% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 50% of the revenue. Determine the monthly revenue needed to break even.

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

Find an equation of the line shown in the figure.

Find the domain of

A cable television firm presently serves 6,600 households and charges $20 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 660 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.

Simplify the difference quotient for

Find an equation of the line that is tangent to the circle x ² + y ² = 25 at the point P ( 3, 4 ).

Sketch the graph of f

Let y = f (x) be a function with domain D = [ -6, -3 ] and range R = [ -8, -2 ]. Find the domain D and range R for the function

An object is projected vertically upward from the top of a building with an initial velocity of ft/sec. Its distance in feet above the ground after seconds is given by the equation Find its maximum distance above the ground.

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 900in ² per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).

Sketch the graph of the equation.

An object is projected vertically upward from the top of a building with an initial velocity of ft/sec. Its distance in feet above the ground after seconds is given by the equation Find its maximum distance above the ground.

Find a formula that expresses the fact that P(x, y) is a distance 4 away from the origin.

Several values of two functions T and S are listed in the following tables: t 0 1 2 3 T(t) 2 3 1 0 X 0 1 2 3 S(x) 1 0 3 2 Find:

Find the midpoint of the segment AB between the points A (- 3, - 5) and B (15, 7)

Find the domain of

Sketch the graph of the equation.

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).