Question

1)According to the table, is the exam grade a function of the number of hours spent studying?

A) Yes, it is a function because no one failed the test.
B) Yes, it is a function because the student who studied more hours made the best grade.
C) Yes, it is a function because the exam grade increases by 2 points for each hour studied.
D) No, it is not a function because the input value of 3 hours has 2 different output values of 78 and 82.

2)Which set of ordered pairs does NOT represent a function?
A) (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
B) (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
C) (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
D) (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)

Answer 1

For #2, B is not a function because there are two outputs for 2. In order to be a function there must only be one output for every input.

I believe the answer to #1 is D for the same reason.

Answer 2

Answer: The correct options are (1). D, (2). B.

Step-by-step explanation: The explanations are as follows:

(1) We are to check whether the exam grade is a function of the hours spent studying according to the table.

Let, 'x' represents the number of hours spent studying and 'f(x)' be the corresponding exam grade.

Then, according to the table, we have

f(1) = 78, f(2) = 80, f(3) = 78, f(3) = 82, f(4) = 84 and f(5) = 86.

We know that a function cannot have two different output values for a single input value.

Here, f(3) = 78, 82.

So, for input value x = 3, there are two output values f(x) = 78, 82.

Therefore, the exam grade is not a function of the number of hours spent studying because the input value of 3 hours has 2 different output values of 78 and 82.

Thus, option (D) is correct.

(2) We are to select the set of ordered pairs does NOT represent a function.

Option (A) is (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8).

Here, each input value corresponds to one and only one output value, so the given set of ordered pairs represents a function.

Option (B) is (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9).

Here, input value '2' corresponds to two different output values '2' and '7', so the given set of ordered pairs does NOT represent a function.

Option (C) is (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4).

Here, each input value corresponds to one and only one output value, so the given set of ordered pairs represents a function.

Option (D) is (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2) .

Here, each input value corresponds to one and only one output value, so the given set of ordered pairs represents a function.

Thus, correct option is (B).

The correct options are (1). D, (2). B.