Part A: Does the table represent a relation that is a function? Justify your answer by using the values shown in the table. (4 points)
Part B: The function f(h) shown below represents the number of tennis matches Diana won each month when she practiced tennis for h hours every day.
If f(h) = 3h + 1
Calculate and interpret the meaning of f(3). (4 points)
Part C: Write an ordered pair to represent the input and output of the function in Part B when Diana practices tennis for b hours every day. (2 points)
There isn't a table in Part A.
This means that if Diana practices for 3 hours she will win 10 tennis matches.
Part B = 10
And for Part C just plug in a number for b and put it in place for x.
For example if she practiced for 2 hours the equation would look like this 3(2)+1 , which equal 7. Make sense?
Part A:
To determine if the table represents a relation that is a function, we need to check if each input has a unique output. Looking at the table values:
Input (h) | Output (f(h))
------------------------
1 | 4
2 | 7
3 | 10
4 | 13
We can see that for each input, there is only one corresponding output. Therefore, the table represents a relation that is a function.
Part B:
To calculate f(3), we substitute h = 3 into the function f(h) = 3h + 1:
f(3) = 3(3) + 1
= 9 + 1
= 10
Interpretation: The value of f(3) is 10. This means that when Diana practices tennis for 3 hours every day, she wins 10 tennis matches each month.
Part C:
The function f(h) represents the number of tennis matches Diana won each month when she practiced tennis for h hours every day. To write an ordered pair to represent the input and output of the function for b hours, we use (b, f(b)).
In this case, the input value is b (representing the number of hours Diana practices tennis each day), and the output value is f(b) (representing the number of tennis matches she wins each month).
Therefore, the ordered pair to represent the input and output for Diana practicing tennis for b hours every day is (b, f(b)).
Part A: To determine whether the table represents a relation that is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). Looking at the table, we can see that each different input value appears only once, which means there are no duplicates in the x-column. Thus, we don't have any input values that map to multiple output values. Therefore, the table does represent a relation that is a function.
Part B: To calculate f(3), we substitute h = 3 into the given function f(h) = 3h + 1:
f(3) = 3(3) + 1
= 9 + 1
= 10
Interpreting the meaning of f(3), it represents the number of tennis matches Diana won each month when she practiced tennis for 3 hours every day. In this case, she won a total of 10 tennis matches.
Part C: The ordered pair represents the input and output of the function f(b) when Diana practices tennis for b hours every day. In this case, we substitute b into the function and write the corresponding ordered pair as follows:
Input value: b
Output value: f(b) = 3b + 1
Therefore, the ordered pair representing the input and output of the function would be (b, 3b + 1).