B Apply

27. Think About a Plan A cube is a solid figure with six square faces. If the edges of a cube have length 1.5 cm, what is the surface area of the cube?
    • What is the relationship between the length of the edges and the area of each face?
    • What is the relationship between the area of one face and the surface area of the whole cube?
28. Geometry Suppose you have a box with a 4 × 4 -in. 4 times 4 , minusin.  square base and variable height h. The surface area of this box is a function of its height. Write a function to represent the surface area. Evaluate the function for h = h equals  6.5 in.

Find the domain and range of each relation, and determine whether it is a function.

29. 
30. 
31. Geometry The volume of a sphere is a function of its radius, V = 4 3 π r 3 . v equals , 4 thirds , pi , r cubed , .  Evaluate the function for the volume of a volleyball with radius 10.5 cm.
32. Car Rental You are considering renting a car from two different rental companies. Proxy car rental company charges $.32 per mile plus an $18 surcharge. YourPal rental company charges $.36 per mile plus a $12 surcharge.
    1. Write a function that shows the cost of renting a car from Proxy.
    2. Write a function that shows the cost of renting a car from YourPal.
    3. Which company offers the better deal for an 820-mile trip?
33. Temperature The relation between degrees Fahrenheit F and degrees Celsius C is described by the function F = 9 5 C + 32 . f equals , 9 fifths c plus 32 . .  In the following ordered pairs, the first element is degrees Celsius and the second element is its equivalent in degrees Fahrenheit. Find the unknown measure in each ordered pair.
    1. (43, m)
    2. ( − 2 , negative 2 comma  n)
    3. (p, 12)
    4. (q, 19)
34. Reasoning Suppose a function pairs items from set A with items from set B. You can say that the function maps into set B. If the function uses every item from set B, the function maps onto set B. Does each function below map the set of whole numbers into or onto the set of whole numbers?
    1. Function f doubles every number.
    2. Function g maps every number to 1 more than that number.
    3. Function h maps every number to itself.
    4. Function j maps every number to its square.

C Challenge

35. Reasoning Given the functions f ( x ) = 3 x − 21 f open x close equals 3 x minus 21  and g(x) = 3 x + 21 , 3 x plus 21 comma  show that the function f ( x ) − g ( x ) f open x close minus g open x close  is a constant for all the values of x.

Determine whether y is a function of x. Explain.

36. y = 3 x − 11 y equals , 3 over x , minus 11
37. y 2 = 3 x − 7 y squared , equals 3 x minus 7
38. x 2 = 3 y + y x squared , equals 3 y plus y

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