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1. Which of the following values could be used for x and would cause the following relation to NOT be a function?

{(3, -1), (-1,5), (2, -4), (6, 2), (x, -9)}
A) x = 5
B) x = 0
C) x = 6
D) x = -4

3. he function C(d) = 8d + 2 represents the cost to order a box of donuts d, including the flat rate shipping charge.

1) What is the cost per box of donuts?
A) $8
B) $10
C) $2
D) $3

b) How much is the flat rate shipping charge?
A) $10
B) $8
C) $3
D) $2
c) How much will the total cost be to order 3 boxes of donuts?
A) $24
B) $14
C) $10
D) $26
d) Does finding C (−2) make sense in the context of this function?
A) Yes, it makes sense because only irrational values are impossible.
B) No, it does not make sense because -2 is not rational.
C) No, it does not make sense because you cannot order -2 boxes of donuts.
D) Yes, it makes sense because that is the cost of shipping.

4. Given f(x) = 4x + 5, evaluate the function for f(2)
A) f (2) = 11
B) f (2) = 13
C) f (2) = 16
D) f (2) = 21

5. The function h(t) = −16t^2 + 75t represents the height of a ball thrown up into the air after t seconds. What does h(5)
A) The time it takes the ball to reach its maximum point is 5 seconds.
B) The height of the ball 5 seconds after it has been thrown.
C) The ball took 5 seconds to hit the ground.
D) The final height is 5 feet.

1 answer

Let's go through each question step by step.

  1. To determine which value of \( x \) would cause the relation to NOT be a function, we need to check if it would create duplicate \( x \)-values. The pair \( (x, -9) \) must lead to a conflicting \( x \) value.

The current pairs are:

  • (3, -1)
  • (-1, 5)
  • (2, -4)
  • (6, 2)

Out of the options:

  • A) \( x = 5 \) (not in the set) - This does NOT conflict
  • B) \( x = 0 \) (not in the set) - This does NOT conflict
  • C) \( x = 6 \) - This conflicts with (6, 2), hence would cause the relation to NOT be a function.
  • D) \( x = -4 \) (not in the set) - This does NOT conflict

Answer: C) \( x = 6 \)

  1. Given the function \( C(d) = 8d + 2 \):
  1. The cost per box of donuts is the coefficient of \( d \):
  • The coefficient of \( d \) in \( C(d) \) is \( 8 \).

Answer: A) $8

b) The flat rate shipping charge is the constant term in the function:

  • The constant term is \( 2 \).

Answer: D) $2

c) To find the total cost to order 3 boxes of donuts, substitute \( d = 3 \) into the function: \[ C(3) = 8(3) + 2 = 24 + 2 = 26 \]

Answer: D) $26

d) Finding \( C(-2) \) refers to ordering -2 boxes, which doesn't make sense in this context (you can't order a negative number of boxes):

Answer: C) No, it does not make sense because you cannot order -2 boxes of donuts.

  1. Given the function \( f(x) = 4x + 5 \), we evaluate \( f(2) \): \[ f(2) = 4(2) + 5 = 8 + 5 = 13 \]

Answer: B) \( f(2) = 13 \)

  1. For the function \( h(t) = -16t^2 + 75t \), evaluating \( h(5) \):
  • The interpretation of \( h(5) \) is to find the height of the ball 5 seconds after it has been thrown. Thus we calculate: \[ h(5) = -16(5)^2 + 75(5) = -16(25) + 375 = -400 + 375 = -25 \] However, the question is how to interpret \( h(5) \) rather than calculate.

Answer: B) The height of the ball 5 seconds after it has been thrown.