Let's go through each question step by step.
- 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) \( x = 6 \)
- Given the function \( C(d) = 8d + 2 \):
- 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.
- Given the function \( f(x) = 4x + 5 \), we evaluate \( f(2) \): \[ f(2) = 4(2) + 5 = 8 + 5 = 13 \]
Answer: B) \( f(2) = 13 \)
- 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.