x -1 -1 -2 -2
y 0 -1 2 3Part 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)
the table does not represent a function, since you have
y(-1) = 0 and y(-1) = -1
All ordered pairs must have a unique x value.
B:
f(h) = 3h+1, so
f(3) = 3(3)+1 = 10
she wins 10 matches if she practices 3 hours a day.
The only question I have is, if she spends all that time practicing, how does she have time for (at least) 10 tennis matches?
C:
f(b) = 3b+1, so the pair is (b,3b+1)
Part A:
To determine if the table represents a relation that is a function, we need to check if there are any repeated x-values with different y-values.
Looking at the table, we see that for each of the x-values (-1, -1, -2, -2), there is only one corresponding y-value (0, -1, 2, 3). There are no repeated x-values with different y-values, so the table does represent a relation that is a function.
Part B:
The function f(h) = 3h + 1 represents the number of tennis matches Diana won each month when she practiced tennis for h hours every day.
To calculate f(3), we substitute h = 3 into the function:
f(3) = 3(3) + 1
= 9 + 1
= 10
So f(3) = 10. This means that if Diana practices tennis for 3 hours every day, she will win 10 tennis matches each month.
Part C:
To write an ordered pair representing the input and output of the function when Diana practices tennis for b hours every day, we use the input b as the x-value and the output (result of the function) as the y-value.
So the ordered pair would be (b, 3b + 1).