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Question 3 A) The cost for an upcoming field trip is $30 per student. The cost of the field trip, in dollars, is a function of the number of students. Select all the possible outputs for the function defined by C(x)=30xC(x)=30x where x is the number of students going on the fieldtrip. (1 point) Responses 30 30 100 100 50 50 90 90 20 20 Question 4 A) The cost for an upcoming field trip is $30 per student. The cost of the field trip, is dollars, is a function of the number of students x. Select ALL the possible inputs (domain) for the function defined by C(x)=30xC(x)=30x where x is number of students attending the field trip. (1 point) Responses 45 45 4.5 4.5 15 15 14 3414 3414 3414 34 22 22 Question 5 A)Select all representations for the domain of a function given by the number of minutes spent studying for this test in the last hour. (1 point) Responses {x| x>60}{x| x>60}{x| x>60}{x| x>60} (0, 60)(0, 60)(0, 60)(0, 60) (60, ∞)(60, ∞)(60, ∞)(60, ∞) [0, 60][0, 60][0, 60][0, 60] {x| x∈R}{x| x∈R}{x| x∈R}{x| x∈R} {x | 0≤ x ≤60}{x | 0≤ x ≤60}{x | 0≤ x ≤60}{x | 0≤ x ≤60} [0, ∞)[0, ∞)[0, ∞)

1 answer

Question 3

Possible Outputs for the Function C(x) = 30x

To find the possible outputs, we will multiply the variable x (number of students) by 30 (cost per student).

Potential calculations for the options:

  • If x = 1 (1 student): C(1) = 30 * 1 = 30
  • If x = 2 (2 students): C(2) = 30 * 2 = 60 (not in the options)
  • If x = 3 (3 students): C(3) = 30 * 3 = 90
  • If x = 4 (4 students): C(4) = 30 * 4 = 120 (not in the options)
  • If x = 5 (5 students): C(5) = 30 * 5 = 150 (not in the options)
  • If x = 10 (10 students): C(10) = 30 * 10 = 300 (not in the options)
  • If x = 20 (20 students): C(20) = 30 * 20 = 600 (not in the options)
  • If x = 100 (100 students): C(100) = 30 * 100 = 3000 (not in the options)
  • If x = 50 (50 students): C(50) = 30 * 50 = 1500 (not in the options)

The outputs listed in the question are: 30, 100, 50, 90, 20

  • Possible outputs for C(x): 30, 90.

Question 4

Possible Inputs (Domain) for the Function C(x) = 30x

In this context, x represents the number of students attending the field trip. The number of students must be a non-negative integer since you cannot have a fraction of a student or a negative number of students.

Evaluating the options:

  • 45 (valid, as it could represent 45 students)
  • 4.5 (not valid as you cannot have half a student)
  • 15 (valid)
  • 14 (valid)
  • 3414 (valid but impractical for a field trip)
  • 34 (valid)
  • 22 (valid)

So, the valid inputs for x (number of students) are 45, 15, 14, 3414, 34, 22 (excluding decimals).

Question 5

Representations for the Domain of a Function Given by Time Spent Studying

The situation describes the number of minutes spent studying in the last hour, which can be between 0 and 60 minutes, inclusive.

Evaluating the options:

  • {x| x>60} (not valid)
  • (0, 60) (not valid as it's not inclusive)
  • (60, ∞) (not valid)
  • [0, 60] (valid, covers entire range including 0 and 60)
  • {x | x∈R} (not valid, as it does not restrict to minutes studying)
  • {x | 0≤ x ≤ 60} (valid, same as above but in set notation)
  • [0, ∞) (not valid)

Valid representations for the domain: [0, 60], {x | 0≤ x ≤ 60}.

Summary of Answers:

  • Question 3 Outputs: 30, 90
  • Question 4 Inputs: 45, 15, 14, 3414, 34, 22
  • Question 5 Representations: [0, 60], {x | 0≤ x ≤ 60}