The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach buys. The situation is represented by the function rule a=14b. a. Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain. b. Suppose the coach spent $98 before tax. How many basketballs did she buy? a. Complete the following table of values. b 0 1 2 3 4 a (Simplify your answers.)
a.
b | a
--|--
0 | 0
1 | 14
2 | 28
3 | 42
4 | 56
b. To find out how many basketballs the coach bought, we need to solve the equation 14b = 98.
Dividing both sides of the equation by 14, we get b = 7.
Therefore, the coach bought 7 basketballs.
a) To create a table of values, we can substitute different values of b into the function rule a = 14b.
b | a
------------------
0 | 0
1 | 14
2 | 28
3 | 42
4 | 56
To graph the function rule, we can plot these points on a coordinate plane.
The graph of the function rule a = 14b is a straight line that passes through the origin (0,0) and has a slope of 14.
b) To find the number of basketballs the coach bought when spending $98 before tax, we can set up the equation:
98 = 14b
To solve for b, divide both sides of the equation by 14:
98 / 14 = b
b = 7
Therefore, the coach bought 7 basketballs.
a. To create a table of values, we can substitute different values for 'b' in the function rule a = 14b and calculate the corresponding values of 'a':
b | a
---------
0 | 0
1 | 14
2 | 28
3 | 42
4 | 56
To graph the function rule, we can plot the values of 'a' on the y-axis, and the values of 'b' on the x-axis. The points (0,0), (1,14), (2,28), (3,42), and (4,56) will represent the data points on the coordinate plane. We can connect these points with a straight line to visualize the function.
b. We are given that the coach spent $98 before tax. We can set up an equation using the function rule to find the number of basketballs the coach bought:
a = 14b (Given function rule)
98 = 14b (Substituting a = 98)
b = 98/14 (Dividing both sides by 14)
b = 7
Therefore, the coach bought 7 basketballs.