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=16b
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
Suppose the coach spent 112$ before tax. How many basketballs did she buy?
To create a table of values for the function rule a=16b, we can assign different values to b and then calculate the corresponding values of a.
| b | a |
|---|---|
| 1 | 16 |
| 2 | 32 |
| 3 | 48 |
| 4 | 64 |
| 5 | 80 |
To graph the function, we can plot the points (b,a) on a coordinate plane. The x-axis represents the number of basketballs (b) and the y-axis represents the amount spent (a).
The graph of the function rule is a straight line passing through the origin (0,0) with a slope of 16.
The graph is continuous because it does not have any breaks or jumps. It consists of all possible values of a, which are the multiples of 16.
To find the number of basketballs the coach bought if she spent $112, we can substitute a=112 into the function and solve for b:
112 = 16b
Dividing both sides by 16 gives:
b = 112/16
b = 7
Therefore, the coach bought 7 basketballs.
To create a table of values for the function rule, we need to substitute different values for the variable 'b' and calculate the corresponding values of 'a' using the formula a = 16b.
Let's assume possible values for 'b' as 0, 1, 2, 3, and so on, and calculate the values of 'a':
When b = 0, a = 16(0) = 0.
When b = 1, a = 16(1) = 16.
When b = 2, a = 16(2) = 32.
When b = 3, a = 16(3) = 48.
We can continue this process to get more values:
When b = 4, a = 16(4) = 64.
When b = 5, a = 16(5) = 80.
When b = 6, a = 16(6) = 96.
Creating a table:
b | a
--------------
0 | 0
1 | 16
2 | 32
3 | 48
4 | 64
5 | 80
6 | 96
To graph the function rule, we need to plot the values of 'b' on the x-axis and the corresponding values of 'a' on the y-axis. Each point on the graph will represent a combination of 'b' and 'a' from the table.
The graph of the function rule a = 16b will be a straight line passing through the origin (0,0) with a slope of 16. It will extend indefinitely in both the positive and negative direction along the x and y axes.
As for the continuity of the graph, a continuous graph means that it is a connected line without any breaks or jumps. In this case, the graph is continuous because it forms a straight line with no interruptions.
Now, let's find out how many basketballs the coach bought when she spent $112 before tax. We can solve for 'b' in the equation a = 16b.
Given a = $112, we substitute this value into the equation:
112 = 16b
Now, let's solve for 'b' by dividing both sides of the equation by 16:
112/16 = b
b = 7
Therefore, the coach bought 7 basketballs when she spent $112 before tax.
To create a table of values for the function rule a=16b, where a represents the amount spent at the sporting goods store and b represents the number of basketballs bought, we can substitute different values of b into the equation and calculate the corresponding values of a.
| b (Number of Basketball) | a (Amount Spent in $) |
|-------------------------|----------------------|
| 1 | 16 |
| 2 | 32 |
| 3 | 48 |
| 4 | 64 |
| 5 | 80 |
| 6 | 96 |
| 7 | 112 |
To graph the function rule a=16b, we can plot the points from the table on a graph, with b on the x-axis and a on the y-axis.
The graph of this function is a straight line that passes through the origin (0,0), and each point on the graph represents a specific combination of b and a.
The graph is continuous as there are an infinite number of possible values for b and a. In this case, we can have any positive value for b (fractional or decimal) which will correspond to a value for a.
To find out how many basketballs the coach has bought if she has spent $112, we can rearrange the equation a=16b as follows:
112 = 16b
Divide both sides of the equation by 16:
112/16 = b
b = 7
Therefore, the coach bought 7 basketballs.