Ask a New Question
Menu

Question 1 A) Is the relation shown in the table a function? x f(x) 3 2 0 1 5 -7 -3 2 (1 point) Responses No, there are multiple outputs with the same input. No, there are multiple outputs with the same input. Yes, every input has one unique output. Yes, every input has one unique output. No, there are multiple inputs with the same output. No, there are multiple inputs with the same output. Yes, every output has one unique input. Yes, every output has one unique input. Question 2 A)Which of the following relations are functions? Select all that are functions.(1 point) Responses (8, 2), (6, 5), (7, -1), (6, 5) (8, 2), (6, 5), (7, -1), (6, 5) (2, 4), (2, 7), (2, -1), (2, 0) (2, 4), (2, 7), (2, -1), (2, 0) (-1, 3), (-4, 3), (-2, 3), (0, 3) (-1, 3), (-4, 3), (-2, 3), (0, 3) (8, 2), (6, -5), (7, -1), (6, 5) (8, 2), (6, -5), (7, -1), (6, 5) Question 3 A)Read the given scenarios. Determine if it is a function or not a function.(4 points) Function Not a Function Input is Student ID number. Output is student age. The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class. Input is the year a group of students graduates from high school. Output is a list of their current salaries. Input is your birthday. Output is number of TVs in your house.

1 answer

Question 1:

To determine if the relation shown in the table is a function, we need to check if each input \( x \) corresponds to exactly one output \( f(x) \).

Given the data:

  • \( f(3) = 2 \)
  • \( f(0) = 1 \)
  • \( f(5) = -7 \)
  • \( f(-3) = 2 \)

In this case, the input \( -3 \) produces the same output \( f(-3) = 2 \) as the input \( 3 \) does. Since there are different inputs (3 and -3) that yield the same output (2), we can conclude:

Response: No, there are multiple outputs with the same input.

Question 2:

Let's analyze each relation to see if they qualify as functions:

  1. (8, 2), (6, 5), (7, -1), (6, 5):

    • Input \( 6 \) corresponds to two outputs \( 5 \) and \( 5 \) (same). This is a function.

  2. (2, 4), (2, 7), (2, -1), (2, 0):

    • Input \( 2 \) corresponds to multiple outputs \( 4, 7, -1, 0 \). This is not a function.

  3. (-1, 3), (-4, 3), (-2, 3), (0, 3):

    • All different inputs correspond to the same output \( 3 \). This is a function.

  4. (8, 2), (6, -5), (7, -1), (6, 5):

    • Input \( 6 \) corresponds to two different outputs \( -5 \) and \( 5 \). This is not a function.

Responses that are functions:

  • (8, 2), (6, 5), (7, -1), (6, 5)
  • (-1, 3), (-4, 3), (-2, 3), (0, 3)

Question 3:

  1. Input is Student ID number. Output is student age.

    • This is a function since each student ID corresponds to one unique age.

  2. The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class.

    • This is not a function, as multiple students of the same age may be in different grade levels.

  3. Input is the year a group of students graduates from high school. Output is a list of their current salaries.

    • This can be considered a function if each year corresponds to a specific group with defined salaries.

  4. Input is your birthday. Output is the number of TVs in your house.

    • This is not a function since different people with the same birthday may have different numbers of TVs.

Final Assessment:

  • Function: Student ID number to student age.
  • Not a Function: Ages of students to their grade levels, and birthday to the number of TVs in your house.
  • Possibly a Function: Year of high school graduation to current salaries.

If you have any more questions or need further clarification, feel free to ask!